A new five-parameter transmuted generalization of the Lomax distribution (TGL) is introduced in this study which is more flexible than current distributions and has become the latest distribution theory trend. Transmuted generalization of Lomax distribution is the name given to the new model. This model includes some previously unknown distributions. The proposed distribution's structural features, closed forms for an rth moment and incomplete moments, quantile, and Rényi entropy, among other things, are deduced. Maximum likelihood estimate based on complete and Type-II censored data is used to derive the new distribution's parameter estimators. The percentile bootstrap and bootstrap-t confidence intervals for unknown parameters are introduced. Monte Carlo simulation research is discussed in order to estimate the characteristics of the proposed distribution using point and interval estimation. Other competitive models are compared to a novel TGL. The utility of the new model is demonstrated using two COVID-19 real-world data sets from France and the United Kingdom.

Generalized progressive hybrid censoring plan proposed to overcome the limitation of the progressive hybrid censoring scheme is that it cannot be applied when very few failures may occur before pre-specified terminal time 𝑇. In this paper, the estimating problems of the model parameters, reliability and hazard rate functions of Nadarajah-Haghighi distribution when a sample is available from generalized progressive hybrid censoring have been considered. The maximum likelihood and Bayes estimators have been obtained for any function of the model parameters. Approximate confidence intervals for the unknown parameters and any function of them are constructed. Using independent gamma informative priors, the Bayes estimators of the unknown parameters are derived under the squared-error loss function. Two approximation techniques, namely: Lindley approximation method and Metropolis Hastings algorithm have been used to carry out the Bayes estimates and also to construct the associate highest posterior density credible intervals. The performance of the proposed methods are evaluated through a Monte Carlo simulation study. To select the optimum censoring scheme among different competing censoring plans, different optimality criteria have been considered. A real-life dataset, representing the failure times of electronic devices, is analyzed to demonstrate how the applicability of the proposed methodologies in real phenomenon.

For the first time and by using an entire sample, we discussed the estimation of the unknown parameters θ 1 , θ 2 , and β and the system of stress-strength reliability R = P Y < X for exponentiated inverted Weibull (EIW) distributions with an equivalent scale parameter supported eight methods. We will use maximum likelihood method, maximum product of spacing estimation (MPSE), minimum spacing absolute-log distance estimation (MSALDE), least square estimation (LSE), weighted least square estimation (WLSE), method of Cramér-von Mises estimation (CME), and Anderson-Darling estimation (ADE) when X and Y are two independent a scaled exponentiated inverted Weibull (EIW) distribution. Percentile bootstrap and bias-corrected percentile bootstrap confidence intervals are introduced. To pick the better method of estimation, we used the Monte Carlo simulation study for comparing the efficiency of the various estimators suggested using mean square error and interval length criterion. From cases of samples, we discovered that the results of the maximum product of spacing method are more competitive than those of the other methods. A two real‐life data sets are represented demonstrating how the applicability of the methodologies proposed in real phenomena.

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In this paper sampling distributions for the maximum likelihood estimators of the Beta-Binomial model are obtained numerically using approximate random numbers from the Beta-Binomial distribution. STATGRAPHICS package is used to obtain the best fitted distributions using Chi-square and Kolmogorov-Smirnov tests.