A new one parameter distribution recently was proposed for modelling lifetime data called half logistic-geometric (HLG) distribution. In this paper, appropriate transformation is considered for HLG distribution and a new distribution is derived called unit half logistic-geometric (UHLG) distribution for modelling bounded data in the interval (0, 1). Some important statistical properties are investigated with a closed form quantile function. Some methods of parameter estimation are introduced to evaluate the distribution parameter and a simulation study is introduced to compare these different methods. A real data application in the insurance field is introduced to show the flexibility of the new distribution modelling such data comparing with other distributions.

Accurate estimation and modeling of infant mortality rates are crucial for public health planning, medical research, and policy-making. Many biological, environmental, and socio-economic factors influence infant mortality. It is essential to employ robust statistical models that can detect the underlying failure patterns. Traditional lifetime models are incapable of capturing infant mortality patterns due to their complexity, particularly when decreasing failure rates occur over time. We introduce the Inverse Power Ailamujia (IPA) and Truncated Inverse Power Ailamujia (TIPA) distributions as a generalizable lifetime model specifically designed to represent decreasing failure rates, making it highly suitable for analyzing infant mortality data. For the mortality studies, it is often not possible to complete data gathering due to the limitations in cost and time, and hence one resorts to a progressive censoring scheme where only a subset of the observed failures is recorded while the remaining units are progressively censored. Progressive censoring with the IPA and TIPA framework is employed to facilitate data collection. The maximum likelihood estimation (MLE) and Bayesian inference are employed to estimate the IPA and TIPA model's unknown parameters under progressive censoring. The Bayesian approach is explored under symmetric squared error and asymmetric LINEX loss functions, providing robust estimation techniques that account for different levels of parameter uncertainty. Additionally, confidence intervals and credible intervals are constructed using bootstrap methods, asymptotic approximations, and Markov Chain Monte Carlo (MCMC) simulations, ensuring the reliability of parameter estimates. The effectiveness of the proposed approach is demonstrated through a two real-world dataset, where the IPA and TIPA models predicts. The findings highlight the advantages of integrating progressive censoring with the IPA and TIPA distributions, offering a practical and computationally efficient tool for modeling.

In this study, we suggest the truncated version of the inverse power Ailamujia distribution, which is more flexible than other well-known distributions. Statistical properties of the new distribution are considered, such as moments, moment generating function, incomplete moments, quantile function, order statistics, and entropy. We discuss various methods of estimation, such as the method of maximum likelihood, methods of least squares and weighted least squares, the method of the maximum product of spacings, the method of Cramer and Von-Mises, methods of Anderson and Darling and right-tail Anderson and Darling, the method of percentiles, and the Bayesian method. Simulation is implemented to study the performance of estimates. We introduce two real data applications, showing that the new distribution can provide better fits than some other corresponding distributions.

In this study, the estimation of parameters of a three‐parameter flexible reduced logarithmic‐inverse Lomax (FRL‐IL) distribution based on progressive type‐II right censored sample is studied. These methods include maximum likelihood estimations (MLEs) and Bayesian estimators. Approximate confidence intervals (ACIs) for the reliability and hazard functions are estimated based on the asymptotic distribution of maximum likelihood estimates (MLEs). In addition, two bootstrap CIs are also proposed. Bayesian estimates are obtained for symmetric and asymmetric loss functions such as squared error loss (SEL) and linear‐exponential (LINEX) loss functions. The Gibbs within Metropolis‐Hasting sampler procedure is applied using the Markov Chain Monte Carlo (MCMC) technique to get the Bayes estimates of the unknown parameters and their credible intervals (CRIs). Finally, a real‐life dataset that represents a group of patients with bladder cancer is considered an application of the proposed methods.

Progressive type-II (Prog-II) censoring schemes are gaining traction in estimating the parameters, and reliability characteristics of lifetime distributions. The focus of this paper is to enhance the accuracy and reliability of such estimations for the inverse power exponentiated Pareto (IPEP) distribution, a flexible extension of the exponentiated Pareto distribution suitable for modeling engineering and medical data. We aim to develop novel statistical inference methods applicable under Prog-II censoring, leading to a deeper understanding of failure time behavior, improved decision-making, and enhanced overall model reliability. Our investigation employs both classical and Bayesian approaches. The classical technique involves constructing maximum likelihood estimators of the model parameters and their bootstrap covariance intervals. Using the Gibbs process constructed by the Metropolis–Hasting sampler technique, the Markov chain Monte Carlo method provides Bayesian estimates of the unknown parameters. In addition, an actual data analysis is carried out to examine the estimation process’s performance under this ideal scheme.