2019 # A New Power Topp–Leone Generated Family of Distributions with Applications

**Abstract:** In this paper, we introduce a new general family of distributions obtained by a subtle combination of two well-established families of distributions: the so-called power Topp–Leone-G and inverse exponential-G families. Its definition is centered around an original cumulative distribution function involving exponential and polynomial functions. Some desirable theoretical properties of the new family are discussed in full generality, with comprehensive results on stochastic ordering, quantile function and relate…

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“…In this Section we give upper and lower estimates for the one-sided Hausdorff approximation of the Heaviside step-function h t0 (t) by means of family (1), where t 0 is the level of the "median".…”

confidence: 99%

“…In this Section we give upper and lower estimates for the one-sided Hausdorff approximation of the Heaviside step-function h t0 (t) by means of family (1), where t 0 is the level of the "median".…”

confidence: 99%

“…The obtained two-sides estimations (see Proposition 1. [1] ) in particular case with usage of the baseline "deterministic-type" (cdf) for α = 0.9; β = 0.3; q = 0.1…”

confidence: 99%

“…The generated new distributions are more flexible in modelling data in practice. Some famous generators families are, Exponentiated -Weibull -generator (Elgarhy et al [2]), the Marshall-Olkin -G family by Marshal and Olkin [3], beta -G family by Eugene et al [4], the generalized odd log logistic -G by Cordeiro et al [5], the generalized transmuted-G by Nofal et al [6], the odd Lindley-G family by Gomes et al [7], a new extended alpha power transformed (APT)-G by Ahmad et al [8], a new APT-G by Elbatal et al [9], a new power Topp-Leone-G by Bantan et al [10], type II general inverse exponential-G by Jamal et al [11], Truncated Inverted Kumaraswamy-G by Bantan et al [12], the exponentiated truncated inverse Weibull-G by Almarashi et al [13], truncated Cauchy power-G by Aldahlan et al [14] and type II power Topp-Leone-G by Bantan et al [15], among others.…”

confidence: 99%

“…Then, the possible values of the new parameter(s) can significantly improve the statistical capabilities of the parent distribution, positively affecting the central and dispersion parameters, asymmetry, kurtosis and weight on the tails. Examples of such families are the exp-G family [35], Weibull-G family [20], Topp-Leone generated (TL-G) family [11], a new extended alpha power transformed-G [6], a new alpha power transformed-G [29], new power TL-G [17], type II general inverse exponential-G [40], truncated inverted Kumaraswamy-G [16], exponentiated truncated inverse Weibull-G [14], odd generalized NH-G [5], type II power TL-G [18] and others.…”

confidence: 99%