Extended Exponential Regression Model: Diagnostics and Application to Mineral Data

In this paper, we reparameterized the extended exponential model based on the mean in order to include covariates and facilitate the interpretation of the coefficients. The model is compared with common models defined in the positive line also reparametrized in the mean. Parameter estimation is approached based on the expectation–maximization algorithm. Furthermore, we discuss residuals and influence diagnostic tools. A simulation study for recovered parameters is presented. Finally, an application illustrating the advantages of the model in a real data set is presented.

Some New Contributions on the Marshall–Olkin Length Biased Lomax Distribution: Theory, Modelling and Data Analysis

The Lomax distribution is arguably one of the most useful lifetime distributions, explaining the developments of its extensions or generalizations through various schemes. The Marshall–Olkin length-biased Lomax distribution is one of these extensions. The associated model has been used in the frameworks of data fitting and reliability tests with success. However, the theory behind this distribution is non-existent and the results obtained on the fit of data were sufficiently encouraging to warrant further exploration, with broader comparisons with existing models. This study contributes in these directions. Our theoretical contributions on the the Marshall–Olkin length-biased Lomax distribution include an original compounding property, various stochastic ordering results, equivalences of the main functions at the boundaries, a new quantile analysis, the expressions of the incomplete moments under the form of a series expansion and the determination of the stress–strength parameter in a particular case. Subsequently, we contribute to the applicability of the Marshall–Olkin length-biased Lomax model. When combined with the maximum likelihood approach, the model is very effective. We confirm this claim through a complete simulation study. Then, four selected real life data sets were analyzed to illustrate the importance and flexibility of the model. Especially, based on well-established standard statistical criteria, we show that it outperforms six strong competitors, including some extended Lomax models, when applied to these data sets. To our knowledge, such comprehensive applied work has never been carried out for this model.

Kumaraswamy inverse Gompertz distribution: Properties and engineering applications to complete, type-II right censored and upper record data

This article proposes and studies a new three-parameter generalized model of the inverse Gompertz distribution, in the so-called Kumaraswamy inverse Gompertz distribution. The main advantage of the new model is that it has "an upside down bathtub-shaped curve hazard rate function" depending upon the shape parameters. Several of its statistical and mathematical properties including quantiles, median, mode, moments, probability weighted moment, entropy function, skewness and kurtosis are derived. Moreover, the reliability and hazard rate functions, mean time to failure, mean residual and inactive lifetimes are also concluded. The maximum likelihood approach is done here to estimate the new model parameters. A simulation study is conducted to examine the performance of the estimators of this model. Finally, the usefulness of the proposed distribution is illustrated with different engineering applications to complete, type-II right censored, and upper record data and it is found that this model is more flexible when it is compared to well-known models in the statistical literature.

Assessment of SNP-SNP interactions by using square contingency table analysis

The evolution of SNP-SNP interactions has become an interesting field in genetic epidemiology. Most of the studies, aimed to analyze the relationship between genetic factors and disease of interest, are focused on single SNP associations. However, for quantitative traits, influenced by the interplay of environmental and more than one genetic factors, interaction between the multi factors should be taken into consideration. In this study, symmetry models for square contingency tables are applied to the cross-classified SNP-SNP interactions data. Results from a genome-wide association analysis of blood pressure are used as a prior evidence for the interacted SNPs.

Slashed Lomax Distribution and Regression Model

In this article, the slashed Lomax distribution is introduced, which is an asymmetric distribution and can be used for fitting thick-tailed datasets. Various properties are explored, such as the density function, hazard rate function, Renyi entropy, r-th moments, and the coefficients of the skewness and kurtosis. Some useful characterizations of this distribution are obtained. Furthermore, we study a slashed Lomax regression model and the expectation conditional maximization (ECM) algorithm to estimate the model parameters. Simulation studies are conducted to evaluate the performances of the proposed method. Finally, two sets of data are applied to verify the importance of the slashed Lomax distribution.

Systematic review on the application of wearable inertial sensors to quantify everyday life motor activity in people with mobility impairments

BACKGROUND

Recent advances in wearable sensor technologies enable objective and long-term monitoring of motor activities in a patient's habitual environment. People with mobility impairments require appropriate data processing algorithms that deal with their altered movement patterns and determine clinically meaningful outcome measures. Over the years, a large variety of algorithms have been published and this review provides an overview of their outcome measures, the concepts of the algorithms, the type and placement of required sensors as well as the investigated patient populations and measurement properties.

METHODS

A systematic search was conducted in MEDLINE, EMBASE, and SCOPUS in October 2019. The search strategy was designed to identify studies that (1) involved people with mobility impairments, (2) used wearable inertial sensors, (3) provided a description of the underlying algorithm, and (4) quantified an aspect of everyday life motor activity. The two review authors independently screened the search hits for eligibility and conducted the data extraction for the narrative review.

RESULTS

Ninety-five studies were included in this review. They covered a large variety of outcome measures and algorithms which can be grouped into four categories: (1) maintaining and changing a body position, (2) walking and moving, (3) moving around using a wheelchair, and (4) activities that involve the upper extremity. The validity or reproducibility of these outcomes measures was investigated in fourteen different patient populations. Most of the studies evaluated the algorithm's accuracy to detect certain activities in unlabeled raw data. The type and placement of required sensor technologies depends on the activity and outcome measure and are thoroughly described in this review. The usability of the applied sensor setups was rarely reported.

CONCLUSION

This systematic review provides a comprehensive overview of applications of wearable inertial sensors to quantify everyday life motor activity in people with mobility impairments. It summarizes the state-of-the-art, it provides quick access to the relevant literature, and it enables the identification of gaps for the evaluation of existing and the development of new algorithms.

Temperature Influences at the Myoelectric Level in the Upper Extremities of the Human Body

Objective:

Nowadays, surface electromyography (sEMG) signals are used for a variety of medical interaction applications along with hardware and software interfaces. These signals require advanced techniques with different approaches that enable processing the sEMG signals acquired in the upper limb muscles of a person.

Methods:

The purpose of this article is to analyze the sEMG signals of the upper limb of a person exposed to temperature changes to envisage its behavior and its nature. The anticipated diagnostic is a key factor in the health field. Therefore, it is very important to develop more precise methods and techniques. For the present study, a heat chamber that allows controlling the temperature of the area where the patient rests his or her hand was designed and implemented. With the appropriate hardware interfaces, the sEMG signals of the hand were registered with MatLab/Simulink software for further analysis. The article explains the analysis and develops knowledge, through a probabilistic approach regarding the change in the sEMG signals.

Results:

The results show that there is an activity in the sEMG signal response due to changes in temperature and it is feasible to detect them using the proposed method.

Conclusion:

This finding contributes to research that seeks to characterize temperature’s effect in the biomedical field.

Scale Mixture of Rayleigh Distribution

In this paper, the scale mixture of Rayleigh (SMR) distribution is introduced. It is proven that this new model, initially defined as the quotient of two independent random variables, can be expressed as a scale mixture of a Rayleigh and a particular Generalized Gamma distribution. Closed expressions are obtained for its pdf, cdf, moments, asymmetry and kurtosis coefficients. Its lifetime analysis, properties and Rényi entropy are studied. Inference based on moments and maximum likelihood (ML) is proposed. An Expectation-Maximization (EM) algorithm is implemented to estimate the parameters via ML. This algorithm is also used in a simulation study, which illustrates the good performance of our proposal. Two real datasets are considered in which it is shown that the SMR model provides a good fit and it is more flexible, especially as for kurtosis, than other competitor models, such as the slashed Rayleigh distribution.

Detection of Filamentous Microorganisms in Fluorescence Microscopy Images

We present a robust, precise image binarization technique for automatically detecting filamentous microorganisms from digital fluorescence microscopy scans, with application to finding the pseudohyphae that are fungal pathogens responsible for Candida vaginitis. This method employs a hybrid constant false positive rate processor that integrates cell average and order statistic detectors, with linear windows at multiple orientation angles. The hypothesis test rule incorporates elongation enhancement and region of interest masking. Our approach achieves the adaptivity to local noise and all possible object orientations. The designed processor is evaluated theoretically and experimentally using clinical images. Successful detection results are demonstrated.

A New Family of Discrete Distributions with Mathematical Properties, Characterizations, Bayesian and Non-Bayesian Estimation Methods

In this work, we propose and study a new family of discrete distributions. Many useful mathematical properties, such as ordinary moments, moment generating function, cumulant generating function, probability generating function, central moment, and dispersion index are derived. Some special discrete versions are presented. A certain special case is discussed graphically and numerically. The hazard rate function of the new class can be “decreasing”, “upside down”, “increasing”, and “decreasing-constant-increasing (U-shape)”. Some useful characterization results based on the conditional expectation of certain function of the random variable and in terms of the hazard function are derived and presented. Bayesian and non-Bayesian methods of estimation are considered. The Bayesian estimation procedure under the squared error loss function is discussed. Markov chain Monte Carlo simulation studies for comparing non-Bayesian and Bayesian estimations are performed using the Gibbs sampler and Metropolis–Hastings algorithm. Four applications to real data sets are employed for comparing the Bayesian and non-Bayesian methods. The importance and flexibility of the new discrete class is illustrated by means of four real data applications.

A New Extended Two-Parameter Distribution: Properties, Estimation Methods, and Applications in Medicine and Geology

In this paper, a new two-parameter generalized Ramos–Louzada distribution is proposed. The proposed model provides more flexibility in modeling data with increasing, decreasing, J-shaped, and reversed-J shaped hazard rate functions. Several statistical properties of the model were derived. The unknown parameters of the new distribution were explored using eight frequentist estimation approaches. These approaches are important for developing guidelines to choose the best method of estimation for the model parameters, which would be of great interest to practitioners and applied statisticians. Detailed numerical simulations are presented to examine the bias and the mean square error of the proposed estimators. The best estimation method and ordering performance of the estimators were determined using the partial and overall ranks of all estimation methods for various parameter combinations. The performance of the proposed distribution is illustrated using two real datasets from the fields of medicine and geology, and both datasets show that the new model is more appropriate as compared to the Marshall–Olkin exponential, exponentiated exponential, beta exponential, gamma, Poisson–Lomax, Lindley geometric, generalized Lindley, and Lindley distributions, among others.

Technology for monitoring everyday prosthesis use: a systematic review

BACKGROUND

Understanding how prostheses are used in everyday life is central to the design, provision and evaluation of prosthetic devices and associated services. This paper reviews the scientific literature on methodologies and technologies that have been used to assess the daily use of both upper- and lower-limb prostheses. It discusses the types of studies that have been undertaken, the technologies used to monitor physical activity, the benefits of monitoring daily living and the barriers to long-term monitoring, with particular focus on low-resource settings.

METHODS

A systematic literature search was conducted in PubMed, Web of Science, Scopus, CINAHL and EMBASE of studies that monitored the activity of prosthesis users during daily-living.

RESULTS

Sixty lower-limb studies and 9 upper-limb studies were identified for inclusion in the review. The first studies in the lower-limb field date from the 1990s and the number has increased steadily since the early 2000s. In contrast, the studies in the upper-limb field have only begun to emerge over the past few years. The early lower-limb studies focused on the development or validation of actimeters, algorithms and/or scores for activity classification. However, most of the recent lower-limb studies used activity monitoring to compare prosthetic components. The lower-limb studies mainly used step-counts as their only measure of activity, focusing on the amount of activity, not the type and quality of movements. In comparison, the small number of upper-limb studies were fairly evenly spread between development of algorithms, comparison of everyday activity to clinical scores, and comparison of different prosthesis user populations. Most upper-limb papers reported the degree of symmetry in activity levels between the arm with the prosthesis and the intact arm.

CONCLUSIONS

Activity monitoring technology used in conjunction with clinical scores and user feedback, offers significant insights into how prostheses are used and whether they meet the user's requirements. However, the cost, limited battery-life and lack of availability in many countries mean that using sensors to understand the daily use of prostheses and the types of activity being performed has not yet become a feasible standard clinical practice. This review provides recommendations for the research and clinical communities to advance this area for the benefit of prosthesis users.

Mutations in sphingolipid metabolism genes are associated with ADHD

Attention deficit hyperactivity disorder (ADHD) is the most prevalent neurodevelopmental disorder in children, with genetic factors accounting for 75-80% of the phenotypic variance. Recent studies have suggested that ADHD patients might present with atypical central myelination that can persist into adulthood. Given the essential role of sphingolipids in myelin formation and maintenance, we explored genetic variation in sphingolipid metabolism genes for association with ADHD risk. Whole-exome genotyping was performed in three independent cohorts from disparate regions of the world, for a total of 1520 genotyped subjects. Cohort 1 (MTA (Multimodal Treatment study of children with ADHD) sample, 371 subjects) was analyzed as the discovery cohort, while cohorts 2 (Paisa sample, 298 subjects) and 3 (US sample, 851 subjects) were used for replication. A set of 58 genes was manually curated based on their roles in sphingolipid metabolism. A targeted exploration for association between ADHD and 137 markers encoding for common and rare potentially functional allelic variants in this set of genes was performed in the screening cohort. Single- and multi-locus additive, dominant and recessive linear mixed-effect models were used. During discovery, we found statistically significant associations between ADHD and variants in eight genes (GALC, CERS6, SMPD1, SMPDL3B, CERS2, FADS3, ELOVL5, and CERK). Successful local replication for associations with variants in GALC, SMPD1, and CERS6 was demonstrated in both replication cohorts. Variants rs35785620, rs143078230, rs398607, and rs1805078, associated with ADHD in the discovery or replication cohorts, correspond to missense mutations with predicted deleterious effects. Expression quantitative trait loci analysis revealed an association between rs398607 and increased GALC expression in the cerebellum.

Bayesian Analysis of Multiplicative Seasonal Threshold Autoregressive Processes

Seasonal fluctuations are  often  found  in many  time  series.   In addition, non-linearity  and  the  relationship  with  other   time series   are  prominent behaviors  of  several,  of  such   series. In this   paper,    we  consider   the modeling  of multiplicative seasonal threshold autoregressive processes with exogenous input (TSARX), which explicitly and simultaneously incorporate multiplicative seasonality and threshold nonlinearity. Seasonality is modeled to  be  stochastic and  regime  dependent.  The  proposed model  is  a  special case  of a  threshold autoregressive process with  exogenous input  (TARX). We  develop   a   procedure  based  on  Bayesian  methods   to   identify  the model,   estimate parameters,  validate  the  model  and  calculate  forecasts. In  the identification stage   of  the  model,   we  present a  statistical test   of regime  dependent multiplicative seasonality.  The proposed methodology is illustrated with a simulated example and applied  to economic empirical data. 

Corrigendum to ``Descriptive Measures of Poisson-Lomax Distribution''

This corrigendum focuses on the correction of numerical results derived from Poisson-Lomax Distribution (PLD) originally proposed by Al-Zahrani & Sagor (2014). Though the mathematical properties and derivations by Al-Zahrani & Sagor (2014) were immaculate but during the execution ofthe R codes using Monte Carlo simulation some anomalies occurred in the calculation of the mean values. The same  anomalies are addressed in thepresent corrigendum. The outcome of the corrigendum will provide basic guidelines for the academia and reviewers of various journals to match thenumerical results with the shape of the probability distribution under study. The results will also emphasize the fact that code writing is a cumbersome process and due diligence be exercised in executing the codes using any programming language. Relevant R codes are appended in Appendix 'A'.

Using Copula Functions to Estimate The AUC for Two Dependent Diagnostic Tests

When performing validation studies on diagnostic classification procedures, one or more biomarkers are typically measured in individuals. Some of these biomarkers may provide better information; moreover, more than one biomarker may be significant and may exhibit dependence between them. This proposal intends to estimate the Area Under the Receiver Operating  Characteristic Curve  (AUC)  for classifying individuals in a screening study. We analyze the dependence between the results of the tests by means of copula-type dependence (using FGM and Gumbel-Barnett copula functions), and studying the respective AUC under this type of dependence. Three different dependence-level values were evaluated for each copula function considered. In most of the reviewed literature, the authors assume a normal model to represent the performance of the biomarkers used for clinical diagnosis. There are situations in which assuming normality is not possible because that model is not suitable for one or both biomarkers. The proposed statistical model does not depend on some distributional assumption for the biomarkers used for diagnosis procedure, and additionally, it is not necessary to observe a strong or moderate linear dependence between them.

Bivariate lifetime models in presence of cure fraction: a comparative study with many different copula functions

In time-to-event studies it is common the presence of a fraction of individuals not expecting to experience the event of interest; these individuals who are immune to the event or cured for the disease during the study are known as long-term survivors. In addition, in many studies it is observed two lifetimes associated to the same individual, and in some cases there exists a dependence structure between them. In these situations, the usual existing lifetime distributions are not appropriate to model data sets with long-term survivors and dependent bivariate lifetimes. In this study, it is proposed a bivariate model based on a Weibull standard distribution with a dependence structure based on fifteen different copula functions. We assumed the Weibull distribution due to its wide use in survival data analysis and its greater flexibility and simplicity, but the presented methods can be adapted to other continuous survival distributions. Three examples, considering real data sets are introduced to illustrate the proposed methodology. A Bayesian approach is assumed to get the inferences for the parameters of the model where the posterior summaries of interest are obtained using Markov Chain Monte Carlo simulation methods and the Openbugs software. For the data analysis considering different real data sets it was assumed fifteen different copula models from which is was possible to find models with satisfactory fit for the bivariate lifetimes in presence of long-term survivors.

A Gamma-Type Distribution with Applications

This article introduces a new probability distribution capable of modeling positive data that present different levels of asymmetry and high levels of kurtosis. A slashed quasi-gamma random variable is defined as the quotient of independent random variables, a generalized gamma is the numerator, and a power of a standard uniform variable is the denominator. The result is a new three-parameter distribution (scale, shape, and kurtosis) that does not present the identifiability problem presented by the generalized gamma distribution. Maximum likelihood (ML) estimation is implemented for parameter estimation. The results of two real data applications revealed a good performance in real settings.

A New Exponential Approach for Reducing the Mean Squared Errors of the Estimators of Population Mean Using Conventional and Non-Conventional Location Parameters

Classes of ratio-type estimators t (say) and ratio-type exponential estimators te (say) of the population mean are proposed, and their biases and mean squared errors under large sample approximation are presented. It is the class of ratio-type exponential estimators te provides estimators more efficient than the ratio-type estimators.

On Phase-I Monitoring of Process Location Parameter with Auxiliary Information-Based Median Control Charts

A control chart is often used to monitor the industrial or services processes to improve the quality of the products. Mostly, the monitoring of location parameters, both in Phase I and Phase II, is done using a mean control chart with the assumption that the process is free from outliers or the estimators are correctly estimated from in-control samples. Generally, there are question marks about such kind of narratives. The performance of the mean chart is highly affected in the presence of outliers. Therefore, the median chart is an attractive alternative to the mean chart in this situation. The control charts are usually implemented in two phases: Phase I (retrospective) and Phase II (prospective/monitoring). The efficiency of any control chart in Phase II depends on the accuracy of control limits obtained from Phase I. The current study focuses on the Phase I analysis of location parameters using median control charts. We examined the performance of different auxiliary information-based median control charts and compared the results with the usual median chart. Standardized variance and relative efficacy are used as performance measures to evaluate the efficiency of median estimators. Moreover, the probability to signal measure is used to evaluate the performance of proposed control charts to detect any potential changes in the process. The results revealed that the proposed auxiliary information based median control charts perform better in Phase I analysis. In addition, a practical illustration of an industrial scenario demonstrated the significance of the proposed control charts, in which the monitoring of concrete compressive strength is emphasized.

Persistent mercury hot spot in Central Europe and Skalka Dam reservoir as a long-term mercury trap

This study aimed to evaluate the relevance of the floodplain pollution sinks of the legacy mercury (Hg) hot spot in Kössein-Röslau river system (east Bavaria, Germany) for further mobilisation and fluvial transport of mercury in suspended particulate matter (SPM), as an important transport medium of Hg in aquatic systems. The channel belt fluvial erosion as the secondary pollution pathway was also considered. The hot spot has originated from the production of Hg compounds such as C₂H₅HgCN and C₆H₅HgCl in Chemical Factory Marktredwitz, and even more than 30 years after the factory abandonment, the Kössein and the Röslau rivers still export polluted fine grained SPM (median 25-35 μm) with mean annual concentrations of 17.4 mg/kg. SPM sampling was performed by floating samplers, supported by floodplain drill cores and by recent channel sediments manually collected along the polluted rivers further. Based on long-term monitoring data set from state enterprise Povodí Ohře, fish in the Skalka Reservoir have had Hg concentrations in their muscles up to 6 mg/kg for at least the last 14 years, exceeding the European maximal limit of 0.5 mg/Hg/kg. In addition, the Hg inventory in the Kössein-Röslau river stretches was therefore calculated; it produced an estimate of ca. 21 t Hg in a 22-km-long channel belt, prone to fluvial remobilisation during floods. Although a major portion of the fluvially transported Hg has yet been trapped by the Skalka Reservoir, the Hg content in the SPM exported farther downstream still varies between 2 and 10 mg/kg Hg. Due to the considerable Hg inventory in the Kössein-Röslau rivers, an improvement will not occur downstream unless specific measures target the secondary pollution mechanism(s).

A weighted negative binomial Lindley distribution with applications to dispersed data

A new discrete distribution is introduced. The distribution involves the negative binomial and size biased negative binomial distributions as sub-models among others and it is a weighted version of the two parameter discrete Lindley distribution. The distribution has various interesting properties, such as bathtub shape hazard function along with increasing/decreasing hazard rate, positive skewness, symmetric behavior, and over- and under-dispersion. Moreover, it is self decomposable and infinitely divisible, which makes the proposed distribution well suited for count data modeling. Other properties are investigated, including probability generating function, ordinary moments, factorial moments, negative moments and characterization. Estimation of the model parameters is investigated by the methods of moments and maximum likelihood, and a performance of the estimators is assessed by a simulation study. The credibility of the proposed distribution over the negative binomial, Poisson and generalized Poisson distributions is discussed based on some test statistics and four real data sets.

Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications

Alizadeh et al. introduced a flexible family of distributions, in the so-called Gompertz-G family. In this article, a discrete analogue of the Gompertz-G family is proposed. We also study some of its distributional properties and reliability characteristics. After introducing the general class, three special models of the new family are discussed in detail. The maximum likelihood method is used for estimating the family parameters. A simulation study is carried out to assess the performance of the family parameters. Finally, the flexibility of the new family is illustrated by means of four genuine datasets, and it is found that the proposed model provides a better fit than the competitive distributions.

Bivariate Burr X Generator of Distributions: Properties and Estimation Methods with Applications to Complete and Type-II Censored Samples

Burr proposed twelve different forms of cumulative distribution functions for modeling data. Among those twelve distribution functions is the Burr X distribution. In statistical literature, a flexible family called the Burr X-G (BX-G) family is introduced. In this paper, we propose a bivariate extension of the BX-G family, in the so-called bivariate Burr X-G (BBX-G) family of distributions based on the Marshall–Olkin shock model. Important statistical properties of the BBX-G family are obtained, and a special sub-model of this bivariate family is presented. The maximum likelihood and Bayesian methods are used for estimating the bivariate family parameters based on complete and Type II censored data. A simulation study was carried out to assess the performance of the family parameters. Finally, two real data sets are analyzed to illustrate the importance and the flexibility of the proposed bivariate distribution, and it is found that the proposed model provides better fit than the competitive bivariate distributions.

A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications

Within the context of flexible parametric families of distributions, much work has been dedicated in recent years to the theme of skew-symmetric distributions, or symmetry-modulated distributions, as we prefer to call them. The present contribution constitutes a review of this area, with special emphasis on multivariate skew-elliptical families, which represent the subset with more immediate impact on applications. After providing background information of the distribution theory aspects, we focus on the aspects more relevant for applied work. The exposition is targeted to non-specialists in this domain, although some general knowledge of probability and multivariate statistics is assumed. Given this aim, the mathematical profile is kept to the minimum required.

Reliability estimation in a multicomponent stress–strength based on unit-Gompertz distribution

Purpose

The purpose of this paper is to estimate the multicomponent reliability by assuming the unit-Gompertz (UG) distribution. Both stress and strength are assumed to have an UG distribution with common scale parameter.

Design/methodology/approach

The reliability of a multicomponent stress–strength system is obtained by the maximum likelihood (MLE) and Bayesian method of estimation. Bayes estimates of system reliability are obtained by using Lindley’s approximation and Metropolis–Hastings (M–H) algorithm methods when all the parameters are unknown. The highest posterior density credible interval is obtained by using M–H algorithm method. Besides, uniformly minimum variance unbiased estimator and exact Bayes estimates of system reliability have been obtained when the common scale parameter is known and the results are compared for both small and large samples.

Findings

Based on the simulation results, the authors observe that Bayes method provides better estimation results as compared to MLE. Proposed asymptotic and HPD intervals show satisfactory coverage probabilities. However, average length of HPD intervals tends to remain shorter than the corresponding asymptotic interval. Overall the authors have observed that better estimates of the reliability may be achieved when the common scale parameter is known.

Originality/value

Most of the lifetime distributions used in reliability analysis, such as exponential, Lindley, gamma, lognormal, Weibull and Chen, only exhibit constant, monotonically increasing, decreasing and bathtub-shaped hazard rates. However, in many applications in reliability and survival analysis, the most realistic hazard rates are upside-down bathtub and bathtub-shaped, which are found in the unit-Gompertz distribution. Furthermore, when reliability is measured as percentage or ratio, it is important to have models defined on the unit interval in order to have plausible results. Therefore, the authors have studied the multicomponent stress–strength reliability under the unit-Gompertz distribution by comparing the MLEs, Bayes estimators and UMVUEs.

Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data

The most suitable statistical method for explaining serial dependency in time series count data is that based on Hidden Markov Models (HMMs). These models assume that the observations are generated from a finite mixture of distributions governed by the principle of Markov chain (MC). Poisson-Hidden Markov Model (P-HMM) may be the most widely used method for modelling the above said situations. However, in real life scenario, this model cannot be considered as the best choice. Taking this fact into account, we, in this paper, go for Generalised Poisson Distribution (GPD) for modelling count data. This method can rectify the overdispersion and underdispersion in the Poisson model. Here, we develop Generalised Poisson Hidden Markov model (GP-HMM) by combining GPD with HMM for modelling such data. The results of the study on simulated data and an application of real data, monthly cases of Leptospirosis in the state of Kerala in South India, show good convergence properties, proving that the GP-HMM is a better method compared to P-HMM.

Use of Nonconventional Dispersion Measures to Improve the Efficiency of Ratio-Type Estimators of Variance in the Presence of Outliers

The use of auxiliary information in survey sampling to enhance the efficiency of the estimators of population parameters is a common phenomenon. Generally, the ratio and regression estimators are developed by using the known information on conventional parameters of the auxiliary variables, such as variance, coefficient of variation, coefficient of skewness, coefficient of kurtosis, or correlation between the study and auxiliary variable. The efficiency of these estimators is dubious in the presence of outliers in the data and a nonsymmetrical population. This study presents improved variance estimators under simple random sampling without replacement with the assumption that the information on some nonconventional dispersion measures of the auxiliary variable is readily available. These auxiliary variables can be the inter-decile range, sample inter-quartile range, probability-weighted moment estimator, Gini mean difference estimator, Downton’s estimator, median absolute deviation from the median, and so forth. The algebraic expressions for the bias and mean square error of the proposed estimators are obtained and the efficiency conditions are derived to compare with the existing estimators. The percentage relative efficiencies are used to numerically compare the results of the proposed estimators with the existing estimators by using real datasets, indicating the supremacy of the suggested estimators.

Type II Topp Leone Power Lomax Distribution with Applications

In many areas of applied sciences, the last step of a study often consists in analyzing in depth the collected data. Among all the kinds of data, the lifetime data are well-known to convey a great deal of information whose capture is necessary to identify one or more key phenomena. In this regards, numerous mathematical models have been proposed, including those based on lifetime distributions. In this paper, we introduce a new four-parameter lifetime distribution based on the type II Topp-Leone-G family and the power Lomax distribution. In comparison to the existing distributions, the new one is characterized by very flexible probability functions: increasing, decreasing, J, and reverse J shapes are observed for the probability density and hazard rate functions, giving first signs on the potential of adaptability of the related model. With this idea in mind, the new distribution is studied in detail, from both the theoretical and applied sides. After showing its main mathematical properties, the related model is investigated with estimation of the parameters by the maximum likelihood method. We applied it to two practical datasets, including the well-know aircraft windshield data. We show that the new model performs better than several modern adversary models, motivating its use in an applied setting.

Lomax exponential distribution with an application to real-life data

In this paper, a new modification of the Lomax distribution is considered named as Lomax exponential distribution (LE). The proposed distribution is quite flexible in modeling the lifetime data with both decreasing and increasing shapes (non-monotonic). We derive the explicit expressions for the incomplete moments, quantile function, the density function for the order statistics etc. The Renyi entropy for the proposed distribution is also obtained. Moreover, the paper discusses the estimates of the parameters by the usual maximum likelihood estimation method along with determining the information matrix. In addition, the potentiality of the proposed distribution is illustrated using two real data sets. To judge the performance of the model, the goodness of fit measures, AIC, CAIC, BIC, and HQIC are used. Form the results it is concluded that the proposed model performs better than the Lomax distribution, Weibull Lomax distribution, and exponential Lomax distribution.