The quasi-xgamma frailty model with survival analysis under heterogeneity problem, validation testing, and risk analysis for emergency care data.

Frailty models are important for survival data because they allow for the possibility of unobserved heterogeneity problem. The problem of heterogeneity can be existed due to a variety of factors, such as genetic predisposition, environmental factors, or lifestyle choices. Frailty models can help to identify these factors and to better understand their impact on survival. In this study, we suggest a novel quasi xgamma frailty (QXg-F) model for the survival analysis. In this work, the test of Rao-Robson and Nikulin is employed to test the validity and suitability of the probabilistic model, we examine the distribution's properties and evaluate its performance in comparison with many relevant cox-frailty models. To show how well the QXg-F model captures heterogeneity and enhances model fit, we use simulation studies and real data applications, including a fresh dataset gathered from an emergency hospital in Algeria. According to our research, the QXg-F model is a viable replacement for the current frailty modeling distributions and has the potential to improve the precision of survival analyses in a number of different sectors, including emergency care. Moreover, testing the ability and the importance of the new QXg-F model in insurance is investigated using simulations via different methods and application to insurance data.

A size-of-loss model for the negatively skewed insurance claims data: applications, risk analysis using different methods and statistical forecasting.

The future values of the expected claims are very important for the insurance companies for avoiding the big losses under uncertainty which may be produced from future claims. In this paper, we define a new size-of-loss distribution for the negatively skewed insurance claims data. Four key risk indicators are defined and analyzed under four estimation methods: maximum likelihood, ordinary least squares, weighted least squares, and Anderson Darling. The insurance claims data are modeled using many competitive models and comprehensive comparison is performed under nine statistical tests. The autoregressive model is proposed to analyze the insurance claims data and estimate the future values of the expected claims. The value-at-risk estimation and the peaks-over random threshold mean-of-order-p methodology are considered.

A novel generalized Weibull Poisson G class of continuous probabilistic distributions with some copulas, properties and applications to real-life datasets.

The current study introduces and examines copula-coupled probability distributions. It explains their mathematical features and shows how they work with real datasets. Researchers, statisticians, and practitioners can use this study's findings to build models that capture complex multivariate data interactions for informed decision-making. The versatility of compound G families of continuous probability models allows them to mimic a wide range of events. These incidents can range from system failure duration to transaction losses to annual accident rates. Due to their versatility, compound families of continuous probability distributions are advantageous. They can simulate many events, even some not well represented by other probability distributions. Additionally, these compound families are easy to use. These compound families can also show random variable interdependencies. This work focuses on the construction and analysis of the novel generalized Weibull Poisson-G family. Combining the zero-truncated-Poisson G family and the generalized Weibull G family creates the compound G family. This family's statistics are mathematically analysed. This study uses Clayton, Archimedean-Ali-Mikhail-Haq, Renyi's entropy, Farlie, Gumbel, Morgenstern, and their modified variations spanning four minor types to design new bivariate type G families. The single-parameter Lomax model is highlighted. Two practical examples demonstrate the importance of the new family.

A New Family of Continuous Probability Distributions.

In this paper, a new parametric compound G family of continuous probability distributions called the Poisson generalized exponential G (PGEG) family is derived and studied. Relevant mathematical properties are derived. Some new bivariate G families using the theorems of "Farlie-Gumbel-Morgenstern copula", "the modified Farlie-Gumbel-Morgenstern copula", "the Clayton copula", and "the Renyi's entropy copula" are presented. Many special members are derived, and a special attention is devoted to the exponential and the one parameter Pareto type II model. The maximum likelihood method is used to estimate the model parameters. A graphical simulation is performed to assess the finite sample behavior of the estimators of the maximum likelihood method. Two real-life data applications are proposed to illustrate the importance of the new family.

A New Parametric Life Distribution with Modified Bagdonavicius-Nikulin Goodness-of-Fit Test for Censored Validation, Properties, Applications, and Different Estimation Methods.

In this paper, we first study a new two parameter lifetime distribution. This distribution includes "monotone" and "non-monotone" hazard rate functions which are useful in lifetime data analysis and reliability. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Renyi entropy, δ-entropy, order statistics and probability weighted moments are derived. Non-Bayesian estimation methods such as the maximum likelihood, Cramer-Von-Mises, percentile estimation, and L-moments are used for estimating the model parameters. The importance and flexibility of the new distribution are illustrated by means of two applications to real data sets. Using the approach of the Bagdonavicius-Nikulin goodness-of-fit test for the right censored validation, we then propose and apply a modified chi-square goodness-of-fit test for the Burr X Weibull model. The modified goodness-of-fit statistics test is applied for the right censored real data set. Based on the censored maximum likelihood estimators on initial data, the modified goodness-of-fit test recovers the loss in information while the grouped data follows the chi-square distribution. The elements of the modified criteria tests are derived. A real data application is for validation under the uncensored scheme.

Validation of Burr XII inverse Rayleigh model via a modified chi-squared goodness-of-fit test.

In this work, we propose a new three parameter distribution called the Burr XII inverse Rayleigh model, this model is a generalization of the inverse Rayleigh distribution using the Burr XII family introduced by Cordeiro et al. [The burr XII system of densities: properties, regression model and applications. J. Stat. Comput. Simul. 88 (2018), pp. 432-456]. After studying the statistical characterization of this model, we construct a modified chi-squared goodness-of-fit test based on the Nikulin-Rao-Robson statistic in the presence of two cases: censored and complete data. We describe the theory and the mechanism of the Y n 2 statistic test which can be used in survival and reliability data analysis. We use the maximum likelihood estimators based on initial non grouped data. Then, we conduct numerical simulations to reinforce the results. For showing the applicability of our model in various fields, we illustrate it and the proposed test by applications to two real data sets for complete data case and two other data sets in the presence of right censored.

The Lindley Weibull Distribution: properties and applications.

We introduce a new three-parameter lifetime model called the Lindley Weibull distribution, which accommodates unimodal and bathtub, and a broad variety of monotone failure rates. We provide a comprehensive account of some of its mathematical properties including ordinary and incomplete moments, quantile and generating functions and order statistics. The new density function can be expressed as a linear combination of exponentiated Weibull densities. The maximum likelihood method is used to estimate the model parameters. We present simulation results to assess the performance of the maximum likelihood estimation. We prove empirically the importance and flexibility of the new distribution in modeling two data sets.