Statistical inference for a general class of distributions with time-varying parameters

Statistical Inference for Multi State Systems under the Generalized Modified Weibull Class

“…Observe that clearly the MWP distribution given in ( 5) is a member of the class (7). In what follows we introduce a generalized cfamily using an arbitrary function H(•), with the MWP distribution as the parent (baseline) distribution function, defined in (6).…”

“…where h(t) = dH(t) dt the pdf associated with H(•). Recall that the baseline distribution of the ( 6) is the MWP distribution given in (5) with parameters a, λ and β, γ ≥ 0 which is denoted by MWP(a, β, γ, λ) and it is obtained if in (6) we take H(t) = 1 − e −at γ e βt .…”

“…where λ > 0 is the shape parameter of the proposed class. Note that additional distributional parameters associated with the parent distribution H(•) may also be involved in (6). The present work concentrates on the family in (6) using a parent continuous distribution function and discuss some of its properties.…”

Editorial to special issue V WCDANM 2018

“…Barbu et al [5] introduce a general class of distributions for independently but not identically distributed random variables, which is claimed to be closed under extrema. The parameter which generates the class is assumed to be time-varying, which underlines relation to parameter dependence models of type [14].…”

Nearest neighbor estimates of Kaniadakis entropy

“…An approximator for the copula function for the studied problem and asymptotical properties regarding the unknown parameters of the model were determined. In [3] Barbu, Karagrigoriu and Makrides were interested in a general class of distributions for independent (yet not necessarily identically distributed) random variables, closed under minima, in which the main parameter involved has been assumed to be time varying with several possible modeling options. It concerns the reliability and survival analysis for describing the time to event or failure.…”