Characterization of Distributions Through Contraction and Dilation of Dual Generalized Order Statistics

Characterization of Continuous Distributions Based on Order Statistics

“…as obtained by Khan and Athar [3]. The Mean Sum of Square (MSE) of the expected values of the failure times of airplane components using exponential distribution is minimum.…”

“…Various approaches are available in literature. For detailed survey one may refer to Khan and Ali [4], Nagaraja [9], Khan and Abu-Salih [5], Balasubramanian and Beg [12], Franco and Ruiz ( [13], [14]), Balasubramanian and Dey [11], López-Blázquez and Moreno-Rebello [6], Wesolowski and Ahsanullah [10], Dembińska and Wesolowski [1], Khan and Abouammoh [2], Athar et al [7], Khan and Athar [3] and references therein.…”

Expectation Properties of Generalized Order Statistics from Poisson Lomax Distribution

“…Proof The necessary part follows from (22). On the other hand, if the relation in ( 32) is satisfied, then on using [7], for ξ(x) = x p , we have…”

“…Also a characterization theorem based on conditional expectation is presented. For related results on characterization, one can see [6], [9], [10], [11], [13], [20], [22] and [28] among others.…”

Moment Properties of Generalized Order Statistics Based on Modified Weighted Rayleigh Distribution

“…In recent years there has been a great interest in the characterization of probability distributions through recurrence relations, conditional expectations and truncation moment. For more detail survey on characterization, one may refer to Galambos and Kotz [18], Kotz and Shanbhag [32], Su and Huang [37], Khan and Abouammoh [24], Khan and Alzaid [25], Khan and Athar [26], Khan et al [27], Ahsanullah [3], Athar…”