Relations for Moments of Generalized Record Values from Additive Weibull Distribution and Associated Inference

Abstract

In this note we give some simple recurrence relations satisfied by single and product moments of k-th upper record values from the additive Weibull distribution. These relations are deduced for moments of upper record values. Further, conditional expectation and recurrence relation for single moments are used to characterize the additive Weibull distribution and some computational works are also carried out.

Expectation Identities of Generalized Record Values From New Weibull-Pareto Distribution and Its Characterization

“…For some recent developments on generalized upper record values with special reference to those arising from exponential, Gumble, Pareto, generalized Pareto, Burr, Weibull, Gompertz, Makeham, exponential-Weibull, modified Weibull, and additive Weibull distributions, see Grudzień and Szynal [7], Pawlas and Szynal [17,18,19], Minimol and Thomas [14,15], Khan et al [13], Khan and Khan [11], and Khan et al [12], respectively. In this work, we mainly focus on the study of generalized upper record values arising from the New Weibull-Pareto distribution.…”

Best Linear Unbiased Estimation and Prediction of Record Values Based on Kumaraswamy Distributed Data

“…Feller [10] gave some examples of record values in gambling. For more reading about the details of the record value and its applications from the point view of the statisticians, the reader can refer to Arnold et al [3], [1], Khan et al [13], and Nevzorov [21]. Record values appears in many real-life events, such as sports, economics, weather, pollution levels, industry and so on.…”

Dual Generalized Order Statistics from Gompertz-Verhulst Distribution and Characterization

“…For example, the development of the general theory of characterizations of probability distributions by conditional expectations began with work of Kotlarski [5], Talwalker [6] and Galambus and Kotz [7] are notable. Further the development on the characterization of probability distributions by conditional expectations continued with the contributions of many authors among them, Gupta and Ahsanullah [8], Zora et al [9], Khan et al [10] and Gupta and Anwar [11] among others. Several authors have utilized the concept of dual generalized order statistics in characterization of distributions including Ahsanullah [12,13], Mbah and Ahasanullah [14], Khan et al [15,16], Faizan and Khan [17], Tavanagar [18], Khan and Faizan [19], Khan and Khan [20] and Khan and Khan [21].…”