The lifetime analysis of the Weibull model based on Generalized Type-I progressive hybrid censoring schemes

<abstract><p>In this study, we estimate the unknown parameters, reliability, and hazard functions using a generalized Type-I progressive hybrid censoring sample from a Weibull distribution. Maximum likelihood (ML) and Bayesian estimates are calculated using a choice of prior distributions and loss functions, including squared error, general entropy, and LINEX. Unobserved failure point and interval Bayesian predictions, as well as a future progressive censored sample, are also developed. Finally, we run some simulation tests for the Bayesian approach and numerical example on real data sets using the MCMC algorithm.</p></abstract>

New extensions of Rayleigh distribution based on inverted-Weibull and Weibull distributions

The Rayleigh distribution was proposed in the fields of acoustics and optics by lord Rayleigh. It has wide applications in communication theory, such as description of instantaneous peak power of received radio signals, i.e. study of vibrations and waves. It has also been used for modeling of wave propagation, radiation, synthetic aperture radar images, and lifetime data in engineering and clinical studies. This work proposes two new extensions of the Rayleigh distribution, namely the Rayleigh inverted-Weibull (RIW) and the Rayleigh Weibull (RW) distributions. Several fundamental properties are derived in this study, these include reliability and hazard functions, moments, quantile function, random number generation, skewness, and kurtosis. The maximum likelihood estimators for the model parameters of the two proposed models are also derived along with the asymptotic confidence intervals. Two real data sets in communication systems and clinical trials are analyzed to illustrate the concept of the proposed extensions. The results demonstrated that the proposed extensions showed better fitting than other extensions and competing models.

On the T-X Class of Topp Leone-G Family of Distributions: Statistical Properties and Applications

This article investigates the T-X class of Topp Leone- G family of distributions. Some members of the new family are discussed. The exponential-Topp Leone-exponential distribution (ETLED) which is one of the members of the family is derived and some of its properties which include central and non-central moments, quantiles, incomplete moments, conditional moments, mean deviation, Bonferroni and Lorenz curves, survival and hazard functions, moment generating function, characteristic function and R`enyi entropy are established. The probability density function (pdf) of order statistics of the model is obtained and the parameter estimation is addressed with the maximum likelihood method (MLE). Three real data sets are used to demonstrate its application and the results are compared with two other models in the literature.

The Kumaraswamy Lindley Regression Model with Application on the Egyptian Stock Exchange

We introduce and study the Kumaraswamy Lindely Distribution (KLD) model, which has increasing, decreasing, upside-down bathtub and bathtub shaped hazard functions.. We perform a Monte Carlo simulation study to assess the finite sample behavior of the maximum likelihood estimates of the parameters. We define a new regression model based on the new distribution. The new regression was applied to data from the Egyptian stock exchange in the period of (2015-2019). Finally, we study some properties of regression Residual analysis The martingale residual, Deviance component residual.

Estimating tails of independently stopped random walks using concave approximations of hazard functions

This paper considers logarithmic asymptotics of tails of randomly stopped sums. The stopping is assumed to be independent of the underlying random walk. First, finiteness of ordinary moments is revisited. Then the study is expanded to more general asymptotic analysis. Results are applicable to a large class of heavy-tailed random variables. The main result enables one to identify if the asymptotic behaviour of a stopped sum is dominated by its increments or the stopping variable. As a consequence, new sufficient conditions for the moment determinacy of compounded sums are obtained.

The Expected Length of Stay At Aged Care Facilities in Australia: Current and Future

This paper analyzes the hazard functions of exiting from an aged care facility in Australia. Using a comprehensive dataset ranging over 2008--2018, we find that those functions are heterogeneous across the age, sex and year-of-leaving. The modelling results lead to in-sample estimated expected length of stay (LOS) for residents differed by age (in general, longer for older groups) and sex (longer for females). The estimated LOS declines gradually from 2008 to 2014 and then steadily increase afterwards for all heterogeneous age and sex groups. Out-of-sample predictions up to 2100 suggest that the longest LOS belongs to females aged 100 and older, with the estimated/predicted LOS increasing from 58.6 months in 2018 to 68.9 months in 2100. Relative uncertainty measures are also provided. Those results can be used to explore the nature of and aspects to improve service quality of Australian aged care facilities for policy makers.

Statistical Inference under Censored Data for the New Exponential-X Fréchet Distribution: Simulation and Application to Leukemia Data

In reliability studies, the best fitting of lifetime models leads to accurate estimates and predictions, especially when these models have nonmonotone hazard functions. For this purpose, the new Exponential-X Fréchet (NEXF) distribution that belongs to the new exponential-X (NEX) family of distributions is proposed to be a superior fitting model for some reliability models with nonmonotone hazard functions and beat the competitive distribution such as the exponential distribution and Frechet distribution with two and three parameters. So, we concentrated our effort to introduce a new novel model. Throughout this research, we have studied the properties of its statistical measures of the NEXF distribution. The process of parameter estimation has been studied under a complete sample and Type-I censoring scheme. The numerical simulation is detailed to asses the proposed techniques of estimation. Finally, a Type-I censoring real-life application on leukaemia patient’s survival with a new treatment has been studied to illustrate the estimation methods, which are well fitted by the NEXF distribution among all its competitors. We used for the fitting test the novel modified Kolmogorov–Smirnov (KS) algorithm for fitting Type-I censored data.