Survival analysis based on an enhanced Rayleigh-inverted Weibull model.

This study proposes a two-parameter survival model based on the Kavya-Manoharan transformation family and the Rayleigh-inverted Weibull distribution, the so-called Kavya-Manoharan-Rayleigh inverted Weibull distribution (KMRIWD). Various reliability measures and statistical properties of this distribution are analyzed. The parameters of the distribution are estimated using the maximum likelihood method and different sampling techniques.

A new extended Fréchet model with different estimation methods and applications.

In this study, we introduce a new extension of the Fréchet distribution known as the new extended Fréchet (NE_Fr) model. The NE_Fr is created by combining the new extended family of distributions and the Fréchet distribution. The NE_Fr has more flexibility than the classical Fréchet distribution and some generalizations of the Fréchet distribution.

An extended Rayleigh Weibull model with actuarial measures and applications.

In this article, we discuss a new extension of the Rayleigh-Weibull model using the Marshall-Olkin family of distributions. The proposed model is called the Marshall-Olkin-Rayleigh-Weibull (MORW) model. Various statistical properties of the MORW distribution are discussed, including explicit expressions for quantiles, moments, incomplete and conditional moments, some inequality measures, moment generating function, moments of the residual and reversed residual life, the Rényi entropy, and order statistics.

Preservation of the aging intensity order and the preservation of the monotonic aging intensity classes under distorted distributions.

This paper presents preservation property of the aging intensity order and the preservation property of the monotonic aging intensity classes under distorted distributions. Several sufficient conditions are given to get the preservation properties. It is shown that the imposed conditions are achievable as we examine in some examples.

Selection effect of learning rate parameter on estimators of exponential populations under the joint hybrid censoring.

A Bayesian method based on the learning rate parameter is called a generalized Bayesian method. In this study, joint hybrid censored type I and type II samples from exponential populations were examined to determine the influence of the parameter on the estimation results. To investigate the selection effects of the learning rate and the loss parameters on the estimation results, we considered two additional loss functions in the Bayesian approach: the linear and the generalized entropy loss functions.

Some New Results Involving Past Tsallis Entropy of Order Statistics.

This work focuses on exploring the properties of past Tsallis entropy as it applies to order statistics. The relationship between the past Tsallis entropy of an ordered variable in the context of any continuous probability law and the past Tsallis entropy of the ordered variable resulting from a uniform continuous probability law is worked out. For order statistics, this method offers important insights into the characteristics and behavior of the dynamic Tsallis entropy, which is associated with past events.

Cumulative Residual Entropy of the Residual Lifetime of a Mixed System at the System Level.

Recently, there has been growing interest in alternative measures of uncertainty, including cumulative residual entropy. In this paper, we consider a mixed system consisting of components, assuming that all components are operational at time . By utilizing the system signature, we are able to compute the cumulative residual entropy of a mixed system's remaining lifetime.

On the Uncertainty Properties of the Conditional Distribution of the Past Life Time.

For a given system observed at time , the past entropy serves as an uncertainty measure about the past life-time of the distribution. We consider a coherent system in which there are components that have all failed at time . To assess the predictability of the life-time of such a system, we use the signature vector to determine the entropy of its past life-time.

Tsallis Entropy of a Used Reliability System at the System Level.

Measuring the uncertainty of the lifetime of technical systems has become increasingly important in recent years. This criterion is useful to measure the predictability of a system over its lifetime. In this paper, we assume a coherent system consisting of components and having a property where at time t, all components of the system are alive.

Further Properties of Tsallis Entropy and Its Application.

The entropy of Tsallis is a different measure of uncertainty for the Shannon entropy. The present work aims to study some additional properties of this measure and then initiate its connection with the usual stochastic order. Some other properties of the dynamical version of this measure are also investigated.

Fractional Survival Functional Entropy of Engineering Systems.

An alternate measure of uncertainty, termed the fractional generalized cumulative residual entropy, has been introduced in the literature. In this paper, we first investigate some variability properties this measure has and then establish its connection to other dispersion measures. Moreover, we prove under sufficient conditions that this measure preserves the location-independent riskier order.

Stochastic Properties of Fractional Generalized Cumulative Residual Entropy and Its Extensions.

The fractional generalized cumulative residual entropy (FGCRE) has been introduced recently as a novel uncertainty measure which can be compared with the fractional Shannon entropy. Various properties of the FGCRE have been studied in the literature. In this paper, further results for this measure are obtained.

Some Further Results on the Fractional Cumulative Entropy.

In this paper, the fractional cumulative entropy is considered to get its further properties and also its developments to dynamic cases. The measure is used to characterize a family of symmetric distributions and also another location family of distributions. The links between the fractional cumulative entropy and the classical differential entropy and some reliability quantities are also unveiled.

Applications of Bladder Cancer Data Using a Modified Log-Logistic Model.

In information science, modern and advanced computational methods and tools are often used to build predictive models for time-to-event data analysis. Such predictive models based on previously collected data from patients can support decision-making and prediction of clinical data. Therefore, a new simple and flexible modified log-logistic model is presented in this paper.

Some new results on bathtub-shaped hazard rate models.

The most common non-monotonic hazard rate situations in life sciences and engineering involves bathtub shapes. This paper focuses on the quantile residual life function in the class of lifetime distributions that have bathtub-shaped hazard rate functions. For this class of distributions, the shape of the α-quantile residual lifetime function was studied.

EM Algorithm for Estimating the Parameters of Weibull Competing Risk Model.

One of the most commonly used models in survival analysis is the additive Weibull model and its generalizations. They are well suited for modeling bathtub-shaped hazard rates that are a natural form of the hazard rate. Although they have some advantages, the maximum likelihood and the least square estimators are biased and have poor performance when the data set contains a large number of parameters.

Further Results on the Proportional Vitalities Model.

In contrast to many survival models such as proportional hazard rates and proportional mean residual lives, the proportional vitalities model has also been introduced in the literature. In this paper, further stochastic ordering properties of a dynamic version of the model with a random vitality growth parameter are investigated. Examples are presented to illustrate different established properties of the model.