A new extended gumbel distribution: Properties and application

Abstract

A robust generalisation of the Gumbel distribution is proposed in this article. This family of distributions is based on the T-X paradigm. From a list of special distributions that have evolved as a result of this family, three separate models are also mentioned in this article. A linear combination of generalised exponential distributions can be used to characterise the density of a new family, which is critical in assessing some of the family’s properties. The statistical features of this family are determined, including exact formulations for the quantile function, ordinary and incomplete moments, generating function, and order statistics. The model parameters are estimated using the maximum likelihood method. Further, one of the unique models has been systematically studied. Along with conventional skewness measures, MacGillivray skewness is also used to quantify the skewness measure. The new probability distribution also enables us to determine certain critical risk indicators, both numerically and graphically. We use a simulated assessment of the suggested distribution, as well as apply three real-world data sets in modelling the proposed model, in order to ensure its authenticity and superiority.

A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental Data

“…Recently, Ref. [39] studied the hazards associated with health in the context of extreme value theory. In this part, we focus the application of the proposed model on three different scenarios, such as real-life environmental, survival and biomedical aspects, on five different data sets, which include rainfall acidity of 40 successive days in the state of Minnesota, the line transect data, the failure time of brake pads for 88 cars, the lengths of power failures (in minutes) and the length of time that 72 guinea pigs lived after receiving an injection of a specific amount of mycobacterium tuberculosis in a medical experiment.…”

Tests of fit for the power function lognormal distribution

“…Therefore, models such as the exponential, Weibull, lognormal, and gamma often occupy a central position because of their demonstrated usefulness in a wide range of situations. Over the years, many models have been developed and applied to lifetime data, including the exponentiated generalized linear exponential distribution [ 4 ], generalized transmuted-G family [ 5 ], modified beta transmuted exponential distribution [ 6 ], extended gumbel distribution [ 7 ], and generalized Marshall-Olkin exponentiated exponential distribution [ 8 ]. We will demonstrate that the PFLC distribution can also be applied to the modeling of lifetime data.…”

Generalized Marshall-Olkin exponentiated exponential distribution: Properties and applications

“…Thus, new distributions and distribution families have been derived in recent years by utilizing existing distributions with derivation methods including transformation, compounding, and exponentiation. The LBeta-G family [ 1 ], Kumaraswamy-G family [ 2 ], Topp-Leone G family [ 3 ], modified beta transmuted-G family [ 4 ], exponentiated Weibull distribution [ 5 ], Odd-Lidney half-logistic distribution [ 6 ], and extended Gumbel distribution [ 7 ] are examples of these types of derived distributions. Among others, the weighted exponential [ 8 ], Nadarajah-Haghighi exponential [ 9 ], exponentiated generalized linear exponential [ 10 ], exponentiated Weibull (EW) [ 11 ], exponentiated Weibull-Poisson (EWP) [ 12 ], extended exponential [ 13 ], α-power transformed generalized exponential [ 14 ], odd exponentiated half-logistic exponential [ 15 ], exponentiated additive Weibull [ 16 ], exponentiated Weibull-exponential [ 17 ], extended odd Weibull exponential (EOWEx) [ 18 ], and bimodal exponential [ 19 ] distributions are extensions of the exponential distribution frequently used in survival analysis.…”