An Extended Cosine Generalized Family of Distributions for Reliability Modeling: Characteristics and Applications with Simulation Study

Mahmood, Zafar; Jawa, Taghreed M.; Sayed-Ahmed, Neveen; Khalil, E. M.; Muse, Abdisalam Hassan; Tolba, Ahlam H.

doi:10.1155/2022/3634698

Cited by 17 publications

(13 citation statements)

References 38 publications

(8 reference statements)

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“…[16] discusses the TIIHLW distribution and its features. When the cause of the failure is known or unknown, the maximum likelihood method is applied; see [17,18]. TIIHLW (α, β, λ) has the cumulative distribution function…”

Section: Tiihlw Distributionmentioning

confidence: 99%

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Inference of Reliability Analysis for Type II Half Logistic Weibull Distribution with Application of Bladder Cancer

Mohamed

Tolba

Almetwally

et al. 2022

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The estimation of the unknown parameters of Type II Half Logistic Weibull (TIIHLW) distribution was analyzed in this paper. The maximum likelihood and Bayes methods are used as estimation methods. These estimators are used to estimate the fuzzy reliability function and to choose the best estimator of the fuzzy reliability function by comparing the mean square error (MSE). The simulation’s results showed that fuzziness is better than reality for all sample sizes, and fuzzy reliability at Bayes predicted estimates is better than the maximum likelihood technique. It produces the lowest average MSE until a sample size of n = 50 is obtained. A simulated data set is applied to diagnose the performance of the two techniques applied here. A real data set is used as a practice for the model discussed and developed the maximum likelihood estimate alternative model of TIIHLW as Topp Leone inverted Kumaraswamy, modified Kies inverted Topp–Leone, Kumaraswamy Weibull–Weibull, Marshall–Olkin alpha power inverse Weibull, and odd Weibull inverted Topp–Leone. We conclude that the TIIHLW is the best distribution fit for this data.

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Section: Tiihlw Distributionmentioning

confidence: 99%

“…Since Equations ( 17)-( 19) cannot be solved analytically, some numerical methods such as Newton's method must be employed to solve Equations ( 17), (18), and (19) and obtain estimates of the parameters α, β , and λ.…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

Inference of Reliability Analysis for Type II Half Logistic Weibull Distribution with Application of Bladder Cancer

Mohamed

Tolba

Almetwally

et al. 2022

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“…The generalised Lindley distribution was first introduced in 2011 by Nadarajah et al, who showed that it outperforms gamma, log-normal, Weibull, and exponential distributions when taking bathtub hazard rate into account [12]. In 2021, Mahmood et al [19] published an enlarged Cosine generalised family of distributions for dependability modelling: characteristics and applications with simulation analysis, and Muse et al [20] suggested a new flexible form of the loglogistic distribution. Citations [5], [17], and [6] in 2022 explored a family of produced distributions with applications.…”

Section: Introductionmentioning

confidence: 99%

Bayesian and Non-Bayesian Estimation Methods for Simulating the Parameter of the Akshaya Distribution

Tolba

2022

Computational Journal of Mathematical and Statistical Sciences

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For modelling lifetime data from biological research and engineering, the "Akshaya distribution" is a model one-parameter continuous distribution that was proposed by [15]. The non-Bayesian and Bayesian estimation methods for the Akshaya's parameter are also presented in this study. The weighted least square estimation (WLSE), least square estimation (LSE), Cramer-von-Mises estimation (CVME), and maximum likelihood estimation (MLE), five traditional estimation approaches, are used to find the model parameter. The parameter of the suggested distribution was also determined using the squared error loss function and Bayesian estimating (BE) under independent gamma priors. Finally, a simulation study is used to expound on the applicability and value of the proposed distribution.

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“…As a baseline hazard rate, many probability distributions for the number of competing causes of the event of interest have been offered. An interesting survey for the classical distributions and their survey can be referred to [30][31][32][33][34][35]. Table 1 shows the chronological review on the competing risk models under progressive censoring scheme with different baseline distributions.…”

Section: Introductionmentioning

confidence: 99%

Estimation for Akshaya Failure Model with Competing Risks under Progressive Censoring Scheme with Analyzing of Thymic Lymphoma of Mice Application

Abushal

Kumar²,

Muse³

et al. 2022

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In several experiments of survival analysis, the cause of death or failure of any subject may be characterized by more than one cause. Since the cause of failure may be dependent or independent, in this work, we discuss the competing risk lifetime model under progressive type-II censored where the removal follows a binomial distribution. We consider the Akshaya lifetime failure model under independent causes and the number of subjects removed at every failure time when the removal follows the binomial distribution with known parameters. The classical and Bayesian approaches are used to account for the point and interval estimation procedures for parameters and parametric functions. The Bayes estimate is obtained by using the Markov Chain Monte Carlo (MCMC) method under symmetric and asymmetric loss functions. We apply the Metropolis–Hasting algorithm to generate MCMC samples from the posterior density function. A simulated data set is applied to diagnose the performance of the two techniques applied here. The data represented the survival times of mice kept in a conventional germ-free environment, all of which were exposed to a fixed dose of radiation at the age of 5 to 6 weeks, which was used as a practice for the model discussed. There are 3 causes of death. In group 1, we considered thymic lymphoma to be the first cause and other causes to be the second. On the base of mice data, the survival mean time (cumulative incidence function) of mice of the second cause is higher than the first cause.

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An Extended Cosine Generalized Family of Distributions for Reliability Modeling: Characteristics and Applications with Simulation Study

Cited by 17 publications

References 38 publications

Inference of Reliability Analysis for Type II Half Logistic Weibull Distribution with Application of Bladder Cancer

Inference of Reliability Analysis for Type II Half Logistic Weibull Distribution with Application of Bladder Cancer

Bayesian and Non-Bayesian Estimation Methods for Simulating the Parameter of the Akshaya Distribution

Estimation for Akshaya Failure Model with Competing Risks under Progressive Censoring Scheme with Analyzing of Thymic Lymphoma of Mice Application

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