Kumaraswamy odd Burr G family of distributions with applications to reliability data

Abstract

We exhibit a general family of distributions named “Kumaraswamy odd Burr G family of distributions” with four additional parameters to generalize any existing baseline distribution. Some statistical properties of the family are derived, including rth moments, mth incomplete moments, moment generating function and entropies. The parameters of the family are estimated by the maximum likelihood (ML) method for complete sam- ples as well as censored samples. Some sub-models of the family are considered and it is noted that their density functions can be symmetric, left-skewed, right-skewed, unimodal, bimodal and their hazard rate functions can be increasing, decreasing, bathtub, upside- down bathtub and J-shaped. Simulation is carried out for one of the sub-models to check the asymptotic behavior of the ML estimates. Applications to reliability (complete and censored) data are carried out to check the usefulness of some sub-models of the family.

A New Extended Generalized Inverse Exponential Distribution: Properties and Applications

“…Usually the standard distributions will be mathematically simpler, and often other members of the family can be constructed from the standard distributions by simple transformations on the underlying standard random variable. Some recent families of distributions are: Kumaraswamy odd Burr G family of distributions by Nasir et al [1], the Marshal-Olkin Odd Lindley-G family of distributions by Jamal et al [2], The Exponentiated Kumaraswamy-G family of distributions by Silva et al [3], the Topp Leone exponentiated G family of distributions by Ibrahim et al [4], The Topp Leone Kumaraswamy-G family of distributions by Ibrahim et al [5], Odd Chen-G family of distributions by Anzagra et al [6], Modi family of continuous probability distributions by Modi et al [7].…”

Characterizations and infinite divisibility of certain 2016 univariate continuous distributions

“…Let X : Ω → (0, ∞) be a continuous random variable and let q 1 (x) = x −1 1 − e −c λ x λ and q 2 (x) = q 1 (x) e −x λ for x > 0. Then, the random variable X has pdf (38) if and only if the function ξ defined in Theorem 1 is of the form…”

The Gamma Kumaraswamy-G family of distributions: theory, inference and applications

“…In particular, the use of this software can easily tackle the problems involved in computing eventual special functions. Among the high impacted families of distributions, there are the beta-G family by Eugene et al (2002) and Jones (2004), the Kumaraswamy-G (Kw-G) family by Cordeiro and de Castro (2011) and Ramos (2014), the Kumaraswamy Poisson-G (Kw-G) family by Ramos (2014), the McDonald-G (Mc-G) family by Alexander et al (2012), the gamma-G type 1 family by Zografos and Balakrishnan (2009) and Amini et al (2014), the gamma-G type 2 family by Ristic and Balakrishnan (2012) and Amini et al (2014), the odd-gamma-G type 3 family by Torabi and Montazari (2012), the logistic-G family by Torabi and Montazari (2014), the odd exponentiated generated (odd exp-G) family by Cordeiro et al (2013), the transformed-transformer (T-X) (Weibull-X and gamma-X) family by Alzaatreh et al (2013a), the exponentiated T-X family by Alzaatreh et al (2013b), the odd Weibull-G family by Bourguignon et al (2014), the exponentiated half-logistic by Cordeiro et al (2014), the T-X{Y}-quantile based approach family by Aljarrah et al (2014), the T-R{Y} family by Alzaatreh et al (2014), the odd Burr-III-G family by Jamal et al (2017), the Kumaraswamy odd Burr-G family by Nasir et al (2018), the generalized odd gamma-G family by Hosseini et al (2018), the truncated Cauchy power-G family by Aldahlan et al (2019) and the type II general inverse exponential-G family by Jamal et al (2020).…”