Abstract
In this paper, we introduce a new there-parameter Rayleigh distribution, called the Marshall-Olkin alpha power Rayleigh (MOAPR) distribution. Some statistical properties of the MOAPR distribution are obtained. The proposed model is characterized based on truncated moments and reverse hazard function. The maximum likelihood and bootstrap estimation methods are considered to estimate the MOPAR parameters. A Monte Carlo simulation study is performed to compare the maximum likelihood and bootstrap estimation methods. Superiority of the MOAPR distribution over some well-known distributions is illustrated by means of two real data sets.
Highlights
In many applied sciences such as medicine, insurance and engineering, among others, modeling and analyzing life testing of data is crucial
This section is devoted to the characterizations of the Marshall-Olkin alpha power Rayleigh (MOAPR) distribution in two directions : (i) based on a relationship between two truncated moments and (ii) in terms of the reverse hazard function
In this subsection we present characterizations of MOAPR distribution in terms of a simple relationship between two truncated moments
Summary
In many applied sciences such as medicine, insurance and engineering, among others, modeling and analyzing life testing of data is crucial. Marshall-Olkin alpha power Rayleigh distribution: Properties, characterizations, estimation and engineering applications. Definition 3: Mahdavi and Kundu (2017) proposed a transformation of the baseline cdf by adding a new parameter to obtain a family of distributions. Nassar et al (2019) proposed a new flexibility family of distributions using the MO-G and AP classes called MarshallOlkin alpha power-G (MOAP-G) family. Almetwally et al (2021) introduced a new Weibull distribution by using MOAP family. (2021) introduced a new extended Weibull distribution by using MOAP family based on Type I and Type II censored samples. We study a new three-parameter distribution, called Marshall-Olkin alpha power Rayleigh (MOAPR) distribution which extends the Rayleigh distribution and provides more flexibility in modeling engineering data.
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