The gamma-Weibull distribution revisited

Abstract

The five parameter gamma-Weibull distribution has been introduced by Leipnik and Pearce (2004). Nadarajah and Kotz (2007) have simplified it into four parameter form, using hypergeometric functions in some special cases. We show that the probability distribution function, all moments of positive order and the characteristic function of gamma-Weibull distribution of a random variable can be explicitely expressed in terms of the incomplete confluent Fox-Wright Psi-function, which is recently introduced by Srivastava and Pogány (2007). In the same time, we generalize certain results by Nadarajah and Kotz that follow as special cases of our findings.

Cold Duplication and Survival Equivalence in the Case of Gamma - Weibull Distributed Composite Systems

“…Finally, the remaining case κ = 1 coincides with the two-parameter gamma-distribution; the approaching parameters are α and β = µ + a, [7].…”

“…for suitably bounded values of |x| in terms of Euler's gamma function: We note that in (7) the empty product means unity see e.g. [17].…”

“…Composite system SEFs are obtained when the systems consist from i.i.c. possessing gamma-Weibull gW (θ ) life-distribution which has been intensively studied by Leipnik and Pearce [4], Nadarajah and Kotz [6] and Pogány and Saxena [7]. Parameter estimation in Weibull models can be seen in [2].…”

The Topp-Leone Odd Burr X-G Family of Distributions: Properties and Applications

“…Evaluation of the models is also carried out using graphical presentations such as the fitted densities, empirical cdf, Kaplan-Meier and probability plots. TLOBX-W distribution was compared with TLOBX-L distribution (in Equation ( 14)), Gamma Weibull (GW) distribution [21], Weibull Lomax (WL) distribution [22], Type I Half Logistic Weibull (TIHLW) distribution [23], Topp-Leone Generalized Exponential (TLGE) distribution [24], Topp-Leone Exponential (TLE) distribution [25] and Generalized odd Burr X-Weibull (GOBXW) distribution [26]. The pdf of the non-nested models are given in Appendix E.…”

The Marshall-Olkin Exponential Weibull Distribution

“…where λ, α, δ > 0 . * * It is worth mentioning that following another approach, that is, renormalizing the product of the gamma and the Weibull distribution's PDF, Leipnik and Pearce [7] introduced a fiveparameter gamma-Weibull distribution; for further results of this type of investigations consult also [12] and [16]. In turn, the independently introduced, different type of PDF proposed by Provost et al [18] is actually a specific case of Leipnik-Pearce type gamma-Weibull distribution.…”