Marshall–Olkin Alpha Power Weibull Distribution: Different Methods of Estimation Based on Type‐I and Type‐II Censoring

Abstract

This paper introduces the new novel four-parameter Weibull distribution named as the Marshall–Olkin alpha power Weibull (MOAPW) distribution. Some statistical properties of the distribution are examined. Based on Type-I censored and Type-II censored samples, maximum likelihood estimation (MLE), maximum product spacing (MPS), and Bayesian estimation for the MOAPW distribution parameters are discussed. Numerical analysis using real data sets and Monte Carlo simulation are accomplished to compare various estimation methods. This novel model’s supremacy upon some famous distributions is explained using two real data sets and it is shown that the MOAPW model can achieve better fits than other competitive distributions.

A New Transmuted Generalized Lomax Distribution: Properties and Applications to COVID‐19 Data

“…In Table 6 , the TGL distribution is fitted to COVID-19 of France country. The TGL model is compared with other competitive models as Mead and Afify [ 16 ] proposed the Burr-XII model (KEBXII) with Kumaraswamy exponentiated, Weibull-Lomax (WL) distribution, Odds Exponential-Pareto IV (OEPIV) distribution proposed by Baharith et al [ 17 ], Marshall–Olkin Alpha power Weibull (MOAPW) by Almetwally et al [ 18 ], Marshall–Olkin Alpha power extended Weibull (MOAPEW) by Almetwally [ 19 ], Marshall–Olkin alpha power inverse Weibull (MOAPIW) by Basheer et al [ 20 ], Marshall–Olkin alpha power Lomax (MOAPL) by Almongy et al [ 21 ], and Gompertz Lomax (GOLOM) distribution by Oguntunde et al [ 11 ]. According to this result, we note that the estimate of TGL has the best measure where it has the smallest value of Cramer-von Mises ( W ∗ ), Anderson-Darling ( A ∗ ), and Kolmogorov- Smirnov (KS) statistic along with its P value.…”

“…Therefore, we decided to find the best mathematical-statistical model for modeling the data of the countries of France and the United Kingdom. There were also many researchers who worked on finding a model for these data, such as Almetwally [ 12 ], Almetwally [ 13 ], Almetwally [ 14 ], and others.…”

Marshall Olkin Alpha Power Extended Weibull Distribution: Different Methods of Estimation based on Type I and Type II Censoring

“…In [16] introduced MOAP inverse exponential distribution. [17] introduced a new Weibull distribution based on MOAP family. In [18], a new logistics differential model is based on the MOAP family.…”

Best Prediction Method for Progressive Type-II Censored Samples under New Pareto Model with Applications

“…Recently, several authors are interested in studying parameter inference of different distributions under progressive Type-II censoring scheme (PC) (see, for example, Kundu [8], Pradhan and Kundu [9], Maurya et al [10], and Bdair et al [11]). In addition, inference with other censoring schemes appeared in literature with different lifetime models, such as hybrid Type-I progressive censoring, adaptive Type-II progressive censoring, Type-II hybrid censoring, and others (see, for example, Bdair and Haj Ahmad [12]; Haj Ahmad et al [13]; Salah et al [14] Almetwally et al [15]; and Sabry et al [16]). Still there is much space for more work with different censoring schemes under new generalized models.…”