The Truncated Burr X-G Family of Distributions: Properties and Applications to Actuarial and Financial Data

An exponentiated XLindley distribution with properties, inference and applications

In this paper, we propose exponentiated XLindley (EXL) distribution. The novel model is adaptable due to the mixt shapes of its density and failure rate functions. The following key statistical properties of EXL distribution are derived: quantile function, moments, hazard function, mean residual life, and Rényi entropy. The parameters are estimated using the maximum likelihood, Anderson Darling, Cramer von Misses, maximum product spacing, ordinary and weighted least square estimation procedures. To examine the behavior of the estimate, Monte Carlo simulation is used. Further Bayesian technique is also utilized to estimate the EXL parameters. The traceplot and Geweke diagnostics are used to track the convergence of simulated processes. The applicability of the EXL distribution is demonstrated by three datasets from different domains such as mortality rate due to COVID-19, precipitation in inches, and failure time for repairable items. The proposed distribution provides efficient results as compared to renowned competitive distributions.

Truncated Weibull-exponential distribution: methods and applications

This paper introduces a truncated Weibull-exponential distribution and provides a thorough insight into its mathematical characteristics. These characteristics include moments, generating functions, inverse distribution function, and entropy. Various measures are also discussed about the distribution's reliability. A simulation study is carried out to assess the stability and consistency of the maximum likelihood estimates of the parameters. Finally, two social sciences data sets are used to assess the distribution's relevance in modeling real-world situations.

A New Truncated Lindley-Generated Family of Distributions: Properties, Regression Analysis, and Applications

We present the truncated Lindley-G (TLG) model, a novel class of probability distributions with an additional shape parameter, by composing a unit distribution called the truncated Lindley distribution with a parent distribution function G(x). The proposed model's characteristics including critical points, moments, generating function, quantile function, mean deviations, and entropy are discussed. Also, we introduce a regression model based on the truncated Lindley-Weibull distribution considering two systematic components. The model parameters are estimated using the maximum likelihood method. In order to investigate the behavior of the estimators, some simulations are run for various parameter settings, censoring percentages, and sample sizes. Four real datasets are used to demonstrate the new model's potential.

Strategies of Modelling Incident Outcomes Using Cox Regression to Estimate the Population Attributable Risk

When the Cox model is applied, some recommendations about the choice of the time metric and the model's structure are often disregarded along with the proportionality of risk assumption. Moreover, most of the published studies fail to frame the real impact of a risk factor in the target population. Our aim was to show how modelling strategies affected Cox model assumptions. Furthermore, we showed how the Cox modelling strategies affected the population attributable risk (PAR). Our work is based on data collected in the North-West Province, one of the two PURE study centres in South Africa. The Cox model was used to estimate the hazard ratio (HR) of mortality for all causes in relation to smoking, alcohol use, physical inactivity, and hypertension. Firstly, we used a Cox model with time to event as the underlying time variable. Secondly, we used a Cox model with age to event as the underlying time variable. Finally, the second model was implemented with age classes and sex as strata variables. Mutually adjusted models were also investigated. A statistical test to the multiplicative interaction term the exposures and the log transformed time to event metric was used to assess the proportionality of risk assumption. The model's fitting was investigated by means of the Akaike Information Criteria (AIC). Models with age as the underlying time variable with age and sex as strata variables had enhanced validity of the risk proportionality assumption and better fitting. The PAR for a specific modifiable risk factor can be defined more accurately in mutually adjusted models allowing better public health decisions. This is not necessarily true when correlated modifiable risk factors are considered.

A New Wavelet-Based Privatization Mechanism for Probability Distributions

In this paper, we propose a new privatization mechanism based on a naive theory of a perturbation on a probability using wavelets, such as a noise perturbs the signal of a digital image sensor. Wavelets are employed to extract information from a wide range of types of data, including audio signals and images often related to sensors, as unstructured data. Specifically, the cumulative wavelet integral function is defined to build the perturbation on a probability with the help of this function. We show that an arbitrary distribution function additively perturbed is still a distribution function, which can be seen as a privatized distribution, with the privatization mechanism being a wavelet function. Thus, we offer a mathematical method for choosing a suitable probability distribution for data by starting from some guessed initial distribution. Examples of the proposed method are discussed. Computational experiments were carried out using a database-sensor and two related algorithms. Several knowledge areas can benefit from the new approach proposed in this investigation. The areas of artificial intelligence, machine learning, and deep learning constantly need techniques for data fitting, whose areas are closely related to sensors. Therefore, we believe that the proposed privatization mechanism is an important contribution to increasing the spectrum of existing techniques.