Flexible Reduced Logarithmic-Inverse Lomax Distribution with Application for Bladder Cancer

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.

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Estimation of Some Lifetime Parameters of Flexible Reduced Logarithmic‐Inverse Lomax Distribution under Progressive Type‐II Censored Data

Buzaridah

Ramadan

El-Desouky

2022

Journal of Mathematics

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On Unit Exponential Pareto Distribution for Modeling the Recovery Rate of COVID-19

et al. 2023

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In 2019, a new lethal and mutant virus (COVID-19) spread around the world, causing the deaths of millions of people. COVID-19 demonstrates that scientists are involved in significant research efforts to face bacteria with less effort than that dedicated to viruses. Since then, engineers and bio-materials scientists have been trying to develop antiviral research and find a suitable effective medication. Strategies and opportunities for interference diagnostics, treatment strategies, and predicting future factors became mandatory. From a statistical point of view, estimating and modelling these factors play an important role in preventing future viral epidemics. In this article, modelling the recovery rate of COVID-19 is investigated through a new distribution which is called the unit exponential Pareto distribution. The new continuous distribution with three parameters displays a prominent level of flexibility to model decreasing, symmetric, and asymmetric data with a monotone failure rate. The recovery rates of COVID-19 in Turkey and France were examined; moreover, milk production data and components’ failure rates are presented for data modeling. The obtained results proved the superiority of the newly suggested model compared to other unit-based distributions. Several statistical features are studied such as the quantile function, the moments, the moment-generating function, some entropy measures, the ordered statistics, the stress–strength, and stochastic ordering. Two classical estimation methods are used in addition to the Bayesian method. The statistical features and estimation analysis are evaluated using numerical and simulation techniques. As a result, we obtain the efficiency of using the Bayesian method over the classical ones, with respect to the bias, average squared error, and the length of confidence intervals for the unknown parameters.

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Optimizing analgesic pain relief time analysis through Bayesian and non-Bayesian approaches to new right truncated Fréchet-inverted Weibull distribution

Nader,

Ramadan,

Ahmad

et al. 2023

MATH

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<abstract><p>This research introduces a novel right-truncated distribution, termed the right truncated Fréchet-inverted Weibull distribution, and elucidates its mathematical properties including density, cumulative, survival and hazard functions. Various statistical attributes such as moments, quantile, mode and moment-generating functions are explored. These properties indicate the efficiency in modeling pain relief time for patients and the number of recoveries of Leukemia patients. Furthermore, estimation techniques, including maximum likelihood and Bayesian methods, are applied to progressive type-Ⅱ right-censored samples to derive parameter estimation of the proposed distribution. Asymptotic properties are employed to approximate confidence intervals for both reliability and hazard functions. Bayesian estimates are refined using both symmetric and asymmetric loss functions. The suitability of the proposed estimation methodologies is validated through simulation studies. The theoretical framework is applied to two real-world lifetime data sets, thereby substantiating their practical utility in medical areas.</p></abstract>

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Flexible Reduced Logarithmic-Inverse Lomax Distribution with Application for Bladder Cancer

Cited by 3 publications

References 27 publications

Estimation of Some Lifetime Parameters of Flexible Reduced Logarithmic‐Inverse Lomax Distribution under Progressive Type‐II Censored Data

Estimation of Some Lifetime Parameters of Flexible Reduced Logarithmic‐Inverse Lomax Distribution under Progressive Type‐II Censored Data

On Unit Exponential Pareto Distribution for Modeling the Recovery Rate of COVID-19

Optimizing analgesic pain relief time analysis through Bayesian and non-Bayesian approaches to new right truncated Fréchet-inverted Weibull distribution

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