Abstract
We propose a new flexible class called the Marshall-Olkin odd Burr III family for generating continuous distributions and derive some of its statistical properties. We provide three special models which accommodate symmetrical, right-skewed and left-skewed shaped densities as well as bathtub, decreasing, increasing, reversed-J shaped and upside-down bathtub failure rate functions. The parameters are estimated by maximum likelihood, least squares and a percentile method. Some simulations investigate the accuracy of the three methods. We illustrate the utility of a special model through three applications to engineering field.
Highlights
There has be an increasing motivation for constructing new generated families of continuous distributions by adding shape parameters to a baseline distribution due to desirable properties of the generated models
Some well-known generated families were introduced recently such as the MarshallOlkin-G (Marshall and Olkin, 1997), exponentiated-G (Gupta et al, 1998), Kumaraswamy-G (Cordeiro and de Castro, 2011), Lomax-G (Cordeiro et al, 2014), Kumaraswamy Marshall-Olkin-G (Alizadeh et al, 2015), odd Burr generalized-G (Alizadeh et al, 2016), generalized odd log-logistic-G (Cordeiro et al, 2017), generalized tan family (Al-Mofleh, 2018), generalized odd Lindley-G (Afify et al, 2019), odd Lomax-G (Cordeiro et al, 2019) and odd Dagum-G (Afify and Alizadeh, 2020) among others
We propose and study a new generator called the Marshall-Olkin odd Burr III-G (MOOB-G) family by taking (1) as the baseline cdf in Equation (3)
Summary
There has be an increasing motivation for constructing new generated families of continuous distributions by adding shape parameters to a baseline distribution due to desirable properties of the generated models. Marshall and Olkin (1997) proposed a general method to construct new models by adding a shape parameter to a specified distribution. Olkin odd Burr III-G (MOOB-G) family by taking (1) as the baseline cdf in Equation (3). The cdf (5) can be explained by combining the Burr III distribution to generate W (x) with the distribution of an unknown geometric number N of independent risk factors or components generated by the baseline odds ratio. If the randomness of the odds ratio Z is modeled by the Burr III distribution given by Equation (1), the cdf of Z can be written as Pr(Z ≤ z) = H (z; b, c, δ). The sub-models of the MOOB-G family can provide symmetrical, left-skewed, symmetrical, rightskewed, and reversed-J densities, and upside-down bathtub, increasing, decreasing, bathtub, and reversed-J shaped hazard rates.
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