Analysis of Milk Production and Failure Data: Using Unit Exponentiated Half Logistic Power Series Class of Distributions

The unit exponentiated half logistic power series (UEHLPS), a family of compound distributions with bounded support, is introduced in this study. This family is produced by compounding the unit exponentiated half logistic and power series distributions. In the UEHLPS class, some interesting compound distributions can be found. We find formulas for the moments, density and distribution functions, limiting behavior, and other UEHLPS properties. Five well-known estimating approaches are used to estimate the parameters of one sub-model, and a simulation study is created. The simulated results show that the maximum product of spacing estimates had lower accuracy measure values than the other estimates. Ultimately, three real data sets from various scientific areas are used to analyze the performance of the new class.

Rate Distortion Theory for Descriptive Statistics

Rate distortion theory was developed for optimizing lossy compression of data, but it also has applications in statistics. In this paper, we illustrate how rate distortion theory can be used to analyze various datasets. The analysis involves testing, identification of outliers, choice of compression rate, calculation of optimal reconstruction points, and assigning "descriptive confidence regions" to the reconstruction points. We study four models or datasets of increasing complexity: clustering, Gaussian models, linear regression, and a dataset describing orientations of early Islamic mosques. These examples illustrate how rate distortion analysis may serve as a common framework for handling different statistical problems.

Statistical Inference of the Half Logistic Modified Kies Exponential Model with Modeling to Engineering Data

The half-logistic modified Kies exponential (HLMKEx) distribution is a novel three-parameter model that is introduced in the current work to expand the modified Kies exponential distribution and improve its flexibility in modeling real-world data. Due to its versatility, the density function of the HLMKEx distribution offers symmetrical, asymmetrical, unimodal, and reversed-J-shaped, as well as increasing, reversed-J shaped, and upside-down hazard rate forms. An infinite linear representation can be used to represent the HLMKEx density. The HLMKEx model’s fundamental mathematical features are obtained, such as the quantile function, moments, incomplete moments, and moments of residuals. Additionally, some measures of uncertainty as well as stochastic ordering are derived. To estimate its parameters, eight estimation methods are used. With the use of detailed simulation data, we compare the performance of each estimating technique and obtain partial and total ranks for the accuracy measures of absolute bias, mean squared error, and mean absolute relative error. The simulation results demonstrate that, in contrast to other competing distributions, the proposed distribution can actually fit the data more accurately. Two actual data sets are investigated in the field of engineering to demonstrate the adaptability and application of the suggested distribution. The findings demonstrate that, in contrast to other competing distributions, the provided distribution can actually fit the data more accurately.

A New Power Topp-Leone distribution with applications to engineering and industry data

We introduced a brand-new member of the family that is going to be referred to as the New Power Topp-Leone Generated (NPTL-G). This new member is one of a kind. Given the major functions that created this new member, important mathematical aspects are discussed in as much detail as possible. We derived some functions for the new one, included the Rényi entropy, the qf, series development, and moment weighted probabilities. Moreover, to estimate the values of the parameters of our model that were not known, we employed the maximum likelihood technique. In addition, two actual datasets from the real world were investigated in order to bring attention to the possible applications of this novel distribution. This new model performs better than three key rivals based on the measurements that were collected.

Weighted power Maxwell distribution: Statistical inference and COVID-19 applications

During the course of this research, we came up with a brand new distribution that is superior; we then presented and analysed the mathematical properties of this distribution; finally, we assessed its fuzzy reliability function. Because the novel distribution provides a number of advantages, like the reality that its cumulative distribution function and probability density function both have a closed form, it is very useful in a wide range of disciplines that are related to data science. One of these fields is machine learning, which is a sub field of data science. We used both traditional methods and Bayesian methodologies in order to generate a large number of different estimates. A test setup might have been carried out to assess the effectiveness of both the classical and the Bayesian estimators. At last, three different sets of Covid-19 death analysis were done so that the effectiveness of the new model could be demonstrated.

Estimation of parameters and quantiles of the Weibull distribution

We propose three new estimators of the Weibull distribution parameters which lead to three new plug-in estimators of quantiles. One of them is a modification of the maximum likelihood estimator and two of them are based on nonparametric estimators of the Gini coefficient. We also make some review of estimators of the Weibull distribution parameters and quantiles. We compare the small sample performance (in terms of bias and mean squared error) of the known and new estimators and extreme quantiles. Based on simulations, we obtain, among others, that the proposed modification of the maximum likelihood estimator of the shape parameter has a smaller bias and mean squared error than the maximum likelihood estimator, and is better or as good as known estimators when the sample size is not very small. Moreover, one of the proposed estimator, based on the nonparametric estimator of the Gini coefficient, leads to good extreme quantiles estimates (better than the maximum likelihood estimator) in the case of small sample sizes.

Evaluating the performance of memory type logarithmic estimators using simple random sampling

In survey research, various types of estimators have been suggested that consider only the current sample information to compute the unknown population parameters. Therefore, we utilize the past sample information along with the current sample information in the form of hybrid exponentially weighted moving averages to suggest the memory type logarithmic estimators for time-based surveys. The expression of the mean square error of the suggested estimators is determined to the first order of approximation. A relative comparison of the suggested estimators with the existing estimators is performed and efficiency conditions are obtained. Further, a simulation study is accomplished using a hypothetically rendered population and a real data illustration to improve the theoretical results. The results of the simulation study and the real data application exhibit that the consideration of past and current sample information meliorates the efficiency of the suggested estimators.

An INAR(1) Time Series Model via a Modified Discrete Burr–Hatke with Medical Applications

This paper introduces a flexible discrete transmuted record type discrete Burr–Hatke (TRT-DBH) model that seems suitable for handling over-dispersion and equi-dispersion in count data analysis. Further to the elegant properties of the TRT-DBH, we propose, in the time series context, a first-order integer-valued autoregressive process with TRT-DBH distributed innovations [TRBH-INAR(1)]. The moment properties and inferential procedures of this new INAR(1) process are studied. Some Monte Carlo simulation experiments are executed to assess the consistency of the parameters of the TRBH-INAR(1) model. To further motivate its purpose, the TRBH-INAR(1) is applied to analyze the series of the COVID-19 deaths in Netherlands and the series of infected cases due to the Tularaemia disease in Bavaria. The proposed TRBH-INAR(1) model yields superior fitting criteria than other established competitive INAR(1) models in the literature. Further diagnostics related to the residual analysis and forecasting based on the TRBH-INAR(1) model are also discussed. Based on modified Sieve bootstrap predictors, we provide integer forecasts of future death of COVID-19 and infected of Tularemia.

Interpretable, predictive spatio-temporal models via enhanced pairwise directions estimation

This article concerns predictive modeling for spatio-temporal data as well as model interpretation using data information in space and time. We develop a novel approach based on supervised dimension reduction for such data in order to capture nonlinear mean structures without requiring a prespecified parametric model. In addition to prediction as a common interest, this approach emphasizes the exploration of geometric information from the data. The method of Pairwise Directions Estimation (PDE) is implemented in our approach as a data-driven function searching for spatial patterns and temporal trends. The benefit of using geometric information from the method of PDE is highlighted, which aids effectively in exploring data structures. We further enhance PDE, referring to it as PDE+, by incorporating kriging to estimate the random effects not explained in the mean functions. Our proposal can not only increase prediction accuracy but also improve the interpretation for modeling. Two simulation examples are conducted and comparisons are made with several existing methods. The results demonstrate that the proposed PDE+ method is very useful for exploring and interpreting the patterns and trends for spatio-temporal data. Illustrative applications to two real datasets are also presented.

Optimal Tuning of Random Survival Forest Hyperparameter with an Application to Liver Disease

Background

Random Forest (RF) is a technique that optimises predictive accuracy by fitting an ensemble of trees to stabilise model estimates. The RF techniques were adapted into survival analysis to model the survival of patients with liver disease in order to identify biomarkers that are highly influential in patient prognostics.

Methods

The methodology of this study begins by applying the classical Cox proportional hazard (Cox-PH) model and three parametric survival models (exponential, Weibull and lognormal) to the published dataset. The study further applied the supervised learning methods of Tuning Random Survival Forest (TRSF) parameters and the conditional inference Forest (Cforest) to optimally predict patient survival probabilities.

Results

The efficiency of these models was compared using the Akaike information criteria (AIC) and integrated Brier score (IBS). The results revealed that the Cox-PH model (AIC = 185.7233) outperforms the three classical models. We further analysed these data to observe the functional relationships that exist between the patient survival function and the covariates using TRSF.

Conclusion

The IBS result of the TRFS demonstrated satisfactory performance over other methods. Ultimately, it was observed from the TRSF results that some of the covariates contributed positively and negatively to patient survival prognostics.

Three-fold utilization of supplementary information for mean estimation under median ranked set sampling scheme

Ranked set sampling (RSS) has created a broad interest among researchers and it is still a unique research topic. It has at long last begun to find its way into practical applications beyond its initial horticultural based birth in the fundamental paper by McIntyre in the nineteenth century. One of the extensions of RSS is median ranked set sampling (MRSS). MRSS is a sampling procedure normally utilized when measuring the variable of interest is troublesome or expensive, whereas it might be easy to rank the units using an inexpensive sorting criterion. Several researchers introduced ratio, regression, exponential, and difference type estimators for mean estimation under the MRSS design. In this paper, we propose three new mean estimators under the MRSS scheme. Our idea is based on three-fold utilization of supplementary information. Specifically, we utilize the ranks and second raw moments of the supplementary information and the original values of the supplementary variable. The appropriateness of the proposed group of estimators is demonstrated in light of both real and artificial data sets based on the Monte-Carlo simulation. Additionally, the performance comparison is also conducted regarding the reviewed families of estimators. The results are empowered and the predominant execution of the proposed group of estimators is seen throughout the paper.

Extreme Value Distributions: An Overview of Estimation and Simulation

The generalized extreme value distribution (GEVD) and various extreme value distributions are commonly applied in air pollution, telecommunications, operational risk management, finance, insurance, material sciences, economics, and hydrology, among many other industries that deal with extreme events. Extreme value distributions (EVDs) typically limit the distribution of maximum and minimum values for many random observations drawn from the same arbitrary distribution. Besides that, it is a crucial method for forecasting future events and emerged as critical method for predicting future events. As a result, prior research is required to select the best estimation method to obtain a reliable value for the parameters of extreme value distributions. This study provides an overview of three-parameter estimation methods based on goodness-of-fit statistics and root mean square error (RMSE). This paper reviewed and compared three estimation methods used to approximate values of parameters for simulated observations taken from the EVD and GEVD. The method of moments (MOMs), maximum likelihood estimator (MLE), and maximum product of spacing (MPS) were the methods investigated in this study. Our findings indicated that the MPS performed better based on the mean square errors (MSEs); meanwhile, the MPS had similar goodness-of-fit statistic values compared to the MLE.

Identifying patterns in amyotrophic lateral sclerosis progression from sparse longitudinal data

The clinical presentation of amyotrophic lateral sclerosis (ALS), a fatal neurodegenerative disease, varies widely across patients, making it challenging to determine if potential therapeutics slow progression. We sought to determine whether there were common patterns of disease progression that could aid in the design and analysis of clinical trials. We developed an approach based on a mixture of Gaussian processes to identify clusters of patients sharing similar disease progression patterns, modeling their average trajectories and the variability in each cluster. We show that ALS progression is frequently nonlinear, with periods of stable disease preceded or followed by rapid decline. We also show that our approach can be extended to Alzheimer's and Parkinson's diseases. Our results advance the characterization of disease progression of ALS and provide a flexible modeling approach that can be applied to other progressive diseases.

Effects of Public and External Health Spending on Out-of-Pocket Payments for Healthcare in Sub-Saharan Africa

Financing healthcare in Sub-Saharan Africa (SSA) is characterized by high levels of out-of-pocket (OOP) payments for healthcare. This renders many individuals vulnerable to poverty and deviates from the Universal Health Coverage (UHC) goal of providing financial protection for healthcare. We examined the relative effects of public and external health spending on OOP healthcare payment in SSA. We used the system generalised method of moments (GMM) estimator and data from the World Bank's World Development Indicators for 43 SSA countries from 2000 to 2017. The results show reductions in OOP payments are higher with increases in public spending than external spending. This means increases in public health spending, compared to external health spending, will increase the pace towards achieving the financial protection goal of UHC in SSA. But since government spending is limited by fiscal space and parliamentary approval, public health spending through social health insurance might provide a regular means of financing healthcare to speed up achieving the financial protection goal in SSA countries.

Multiparametric MR radiomics in brain glioma: models comparation to predict biomarker status

Background

Genotype status of glioma have important significance to clinical treatment and prognosis. At present, there are few studies on the prediction of multiple genotype status in glioma by method of multi-sequence radiomics. The purpose of the study is to compare the performance of clinical features (age, sex, WHO grade, MRI morphological features etc.), radiomics features from multi MR sequence (T2WI, T1WI, DWI, ADC, CE-MRI (contrast enhancement)), and a combined multiple features model in predicting biomarker status (IDH, MGMT, TERT, 1p/19q of glioma.

Methods

In this retrospective analysis, 81 glioma patients confirmed by histology were enrolled in this study. Five MRI sequences were used for radiomic feature extraction. Finally, 107 features were extracted from each sequence on Pyradiomics software, separately. These included 18 first-order metrics, such as the mean, standard deviation, skewness, and kurtosis etc., 14 shape features and second-order metrics including 24 grey level run length matrix (GLCM), 16 grey level run length matrix (GLRLM), 16 grey level size zone matrix (GLSZM), 5 neighboring gray tone difference matrix (NGTDM), and 14 grey level dependence matrix (GLDM). Then, Univariate analysis and LASSO (Least absolute shrinkage and selection operator regression model were used to data dimension reduction, feature selection, and radiomics signature building. Significant features (p < 0.05 by multivariate logistic regression were retained to establish clinical model, T1WI model, T2WI model, T1 + C (T1WI contrast enhancement model, DWI model and ADC model, multi sequence model. Clinical features were combined with multi sequence model to establish a combined model. The predictive performance was validated by receiver operating characteristic curve (ROC analysis and decision curve analysis (DCA).

Results

The combined model showed the better performance in some groups of genotype status among some models (IDH AUC = 0.93, MGMT AUC = 0.88, TERT AUC = 0.76). Multi sequence model performed better than single sequence model in IDH, MGMT, TERT. There was no significant difference among the models in predicting 1p/19q status. Decision curve analysis showed combined model has higher clinical benefit than multi sequence model.

Conclusion

Multi sequence model is an effective method to identify the genotype status of cerebral glioma. Combined with clinical models can better distinguish genotype status of glioma.

Key Points

The combined model showed the higher performance compare with other models in predicting genotype status of IDH, MGMT, TERT.

Multi sequence model showed a better predictive model than that of a single sequence model.

Compared with other models, the combined model and multi sequence model show no advantage in prediction of 1p/19q status.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12880-022-00865-8.

Poisson Extended Exponential Distribution with Associated INAR(1) Process and Applications

The significance of count data modeling and its applications to real-world phenomena have been highlighted in several research studies. The present study focuses on a two-parameter discrete distribution that can be obtained by compounding the Poisson and extended exponential distributions. It has tractable and explicit forms for its statistical properties. The maximum likelihood estimation method is used to estimate the unknown parameters. An extensive simulation study was also performed. In this paper, the significance of the proposed distribution is demonstrated in a count regression model and in a first-order integer-valued autoregressive process, referred to as the INAR(1) process. In addition to this, the empirical importance of the proposed model is proved through three real-data applications, and the empirical findings indicate that the proposed INAR(1) model provides better results than other competitive models for time series of counts that display overdispersion.

Online water quality monitoring based on UV-Vis spectrometry and artificial neural networks in a river confluence near Sherfield-on-Loddon

Water quality monitoring is very important in agricultural catchments. UV-Vis spectrometry is widely used in place of traditional analytical methods because it is cost effective and fast and there is no chemical waste. In recent years, artificial neural networks have been extensively studied and used in various areas. In this study, we plan to simplify water quality monitoring with UV-Vis spectrometry and artificial neural networks. Samples were collected and immediately taken back to a laboratory for analysis. The absorption spectra of the water sample were acquired within a wavelength range from 200 to 800 nm. Convolutional neural network (CNN) and partial least squares (PLS) methods are used to calculate water parameters and obtain accurate results. The experimental results of this study show that both PLS and CNN methods may obtain an accurate result: linear correlation coefficient (R²) between predicted value and true values of TOC concentrations is 0.927 with PLS model and 0.953 with CNN model, R² between predicted value and true values of TSS concentrations is 0.827 with PLS model and 0.915 with CNN model. CNN method may obtain a better linear correlation coefficient (R²) even with small number of samples and can be used for online water quality monitoring combined with UV-Vis spectrometry in agricultural catchment.

Asymptotic properties of duration-based VaR backtests

To increase the power of the VaR tests, it has been recently proposed to extend the duration-based test class with the geometric-VaR and Gini-coefficient-based tests. These tests, though exhibiting outstanding power properties, have not gained recognition in the industry. A potential reason is the absence of ready-to-use statistical distributions. To remedy this, we inquire into the limiting properties of these tests and derive relevant asymptotic distributions. We also provide a generalized geometric-VaR test and give its distribution. Through the Monte Carlo study, we show the accuracy of our asymptotic procedures in finite samples, and we find these procedures to be relevant for the current Basel standards. Our theoretical results are illustrated by the empirical study that includes data from the current COVID-19 crisis.

A Lindley-Type Distribution for Modeling High-Kurtosis Data

This article proposes a heavy-tailed distribution for modeling positive data. The proposal arises with the ratio of independent random variables, specifically, a Lindley distribution divided by a beta distribution. This leads to a three-parameter extension of the Lindley distribution capable of modeling high levels of kurtosis. The main structural properties of the proposed distribution are derived. The skewness and kurtosis behavior of the distribution are described. Parameter estimation is discussed under consideration of the moment and maximum likelihood methods. Finally, in order to avoid the parameter non-identifiability problem, a two-parameter version of the proposed distribution is derived. The usefulness of this special case is illustrated by fitting data in two real scenarios.

[Multidimensional analysis of the evolution of the COVID-19 pandemic in countries of the AmericasAnálise multidimensional da evolução da pandemia da COVID-19 em países das Américas]

Objetivo.

Evaluar la evolución de pandemia de la COVID-19 entre los países de las Américas, comparando datos de los sistemas de salud previo a la llegada del virus a la Región, frente a los casos y muertes acumuladas antes del despliegue de las estrategias de inmunización de la población, y el estado actual de la vacunación.

Métodos.

Se realizo un análisis multivariante HJ-Biplot y análisis de cluster, para 28 países de la Región de las Américas, en tres momentos del tiempo: diciembre de los años 2019, 2020 y 2021.

Resultados.

En el continente americano se observa heterogeneidad en las acciones implementadas para contener la pandemia, la cual se refleja en diferentes grupos de naciones.

Conclusiones.

No todos los países de la Región de las Américas contaban con las condiciones de salubridad necesarias para afrontar la contención de la COVID-19. A cierre de 2019 Estados Unidos, Canadá, Brasil y Cuba se observaban con ventajas frente a los demás países de la Región, sin embargo, la pertinencia de las acciones implementadas durante el año 2020 para contener la pandemia, generaron diferentes grupos de países según la prevalencia de contagios y muertes. En tal momento, Bolivia, Ecuador y México, presentaban niveles críticos de letalidad. A cierre de 2021, tras la implementación de los planes de vacunación, Argentina, Brasil, Canadá, Chile, Colombia, Costa Rica, Cuba, Panamá, Estados Unidos y Uruguay registran más del 60% de su población con el esquema de vacunación completo.

Exponentiated Odd Lomax Exponential distribution with application to COVID-19 death cases of Nepal

This study suggested a new four-parameter Exponentiated Odd Lomax Exponential (EOLE) distribution by compounding an exponentiated odd function with Lomax distribution as a generator. The proposed model is unimodal and positively skewed whereas the hazard rate function is monotonically increasing and inverted bathtubs. Some important properties of the new distribution are derived such as quintile function and median; asymptotic properties and mode; moments; mean residual life, mean path time; mean deviation; order statistics; and Bonferroni & Lorenz curve. The value of the parameters is obtained from the maximum likelihood estimation, least-square estimation, and Cramér-Von-Mises methods. Here, a simulation study and two real data sets, “the number of deaths per day due to COVID-19 of the first wave in Nepal" and ‘‘failure stresses (In Gpa) of single carbon fibers of lengths 50 mm", have been applied to validate the different theoretical findings. The finding of an order of COVID-19 deaths in 153 days in Nepal obey the proposed distribution, it has a significantly positive relationship between the predictive test positive rate and the predictive number of deaths per day. Therefore, the intended model is an alternative model for survival data and lifetime data analysis.

A new extended gumbel distribution: Properties and application

A robust generalisation of the Gumbel distribution is proposed in this article. This family of distributions is based on the T-X paradigm. From a list of special distributions that have evolved as a result of this family, three separate models are also mentioned in this article. A linear combination of generalised exponential distributions can be used to characterise the density of a new family, which is critical in assessing some of the family’s properties. The statistical features of this family are determined, including exact formulations for the quantile function, ordinary and incomplete moments, generating function, and order statistics. The model parameters are estimated using the maximum likelihood method. Further, one of the unique models has been systematically studied. Along with conventional skewness measures, MacGillivray skewness is also used to quantify the skewness measure. The new probability distribution also enables us to determine certain critical risk indicators, both numerically and graphically. We use a simulated assessment of the suggested distribution, as well as apply three real-world data sets in modelling the proposed model, in order to ensure its authenticity and superiority.

The Slashed Power Half-Normal Distribution with Applications

In this paper, an extension of the power half-normal (PHN) distribution is introduced. This new model is built on the application of slash methodology for positive random variables. The result is a distribution with greater kurtosis than the PHN; i.e., its right tail is heavier than the PHN distribution. Its probability density, survival and hazard rate function are studied, and moments, skewness and kurtosis coefficientes are obtained, along with relevant properties of interest in reliability. It is also proven that the new model can be expressed as the scale mixture of a PHN and a uniform distribution. Moreover, the new model holds the PHN distribution as a limit case when the new parameter tends to infinity. The parameters in the model are estimated by the method of moments and maximum likelihood. A simulation study is given to illustrate the good behavior of maximum likelihood estimators. Two real applications to survival and fatigue fracture data are included, in which our proposal outperforms other models.

A novel extended model with versatile shaped failure rate: Statistical inference with Covid -19 applications

Statistical models perform an essential role in data analysis, and statisticians are constantly looking for novel or pretty recent statistical models to fit data sets across a broad variety of fields. In this study, we used modified Kies generalized transformation and the new power function to suggest an unique statistical model. We present and discuss a linear illustration of the density function. Theoretically, quantile function, characteristic function, stochastic ordering, mean, and moments are just a few of the structure properties we discuss. By defining an ideal statistical distribution for assessing the COVID-19 mortality rate, an attempt is performed to determine the model of COVID-19 spread in different nations like the United Kingdom and Italy. In some countries, the novel distribution have been shown to be more appropriate than existing competing models when fitted to COVID-19.

A new versatile modification of the Rayleigh distribution for modeling COVID-19 mortality rates

The aim of this paper is to specify a new flexible statistical model to analyze COVID-19 mortality rates in Italy and Canada. A new versatile lifetime distribution with four parameters is proposed by using the exponentiated generalized class of distributions and the gull alpha power Rayleigh distribution to form the exponentiated generalized gull alpha power Rayleigh (EGGAPR) distribution. This new distribution is characterized by a tractable cumulative distribution function. To estimate the unknown parameters of the proposed distribution the maximum likelihood estimation method is used. In evaluating the effectiveness of the MLE method graphical displays of the Monte Carlo simulation are presented. The EGGAPR distribution is compared to its sub-models which include the exponentiated gull alpha Rayleigh distribution, the gull alpha Rayleigh distribution, exponentiated generalized Rayleigh distribution, exponentiated Rayleigh distribution and the Rayleigh distribution. Different measures of goodness-of-fit are used to investigate whether the EGGAPR distribution is more flexible and fit than its sub-models in modeling COVID-19 mortality rates.

Survival analysis of cancer patients using a new extended Weibull distribution

One of the most important applications of statistical analysis is in health research and applications. Cancer studies are mostly required special statistical considerations in order to find the appropriate model for fitting the survival data. Existing classical distributions rarely fit such data well and an increasing interest has been shown recently in developing more flexible distributions by introducing some additional parameters to the basic model. In this paper, a new five-parameters distribution referred as alpha power Kumaraswamy Weibull distribution is introduced and studied. Particularly, this distribution extends the Weibull distribution based on a novel technique that combines two well known generalisation methods, namely, alpha power and T-X transformations. Different characteristics of the proposed distribution, including moments, quantiles, Rényi entropy and order statistics are obtained. The method of maximum likelihood is applied in order to estimate the model parameters based on complete and censored data. The performance of these estimators are examined via conducting some simulation studies. The potential importance and applicability of the proposed distribution is illustrated empirically by means of six datasets that describe the survival of some cancer patients. The results of the analysis indicated to the promising performance of the alpha power Kumaraswamy Weibull distribution in practice comparing to some other competing distributions.

Inflated Unit-Birnbaum-Saunders Distribution

The modeling different data behaviour like the human development index as a function of life expectancy, the water capacity of a reservoir with respect to a certain threshold, or the percentage of death rate of an infant before his or her first birthday, are situations which a researcher can face. It is noteworthy that these problems may have in common data with excessive zeros and ones. Then, it is essential to have flexible and accuracy models to fit data with these features. Given the relevance of data modeling with excessive zeros and ones, in this paper, a mixture of discrete and continuous distributions is proposed for modeling data with these behaviors. Additionally, the Unit-Birnbaum-Saunders distribution is considered with the aim to explain the continuous component of the model and the features of a Bernoulli process. The estimation of the parameters is based on the maximum likelihood method. Observed and expected information matrices are derived, illustrating interesting aspects of the likelihood approach. Finally, with practical applications by using real data we can show the advantage of using our proposal concerning the inflated beta model.