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.
Highlights
The statistical study of record values in a sequence of independent and identically distributed continuous random variables was first carried out by Chandler [5]
Dziubdziela and Kopocinski [7] have generalized the concept of record values of Chandler [5] by random variables of a more generalized nature and we may call them as generalized record values or k-th record values
Record values and associated statistics are of great importance in several real life problems involving weather, economic studies, sports and so on
Summary
The statistical study of record values in a sequence of independent and identically distributed (iid) continuous random variables was first carried out by Chandler [5]. Serious difficulties arise if expected values of inter arrival time of records is infinite and occurrences of records are very rare in practice This problem is avoided once we consider the model of k-th record statistics. In this work we mainly focus on the study of generalized record values arising from the additive Weibull distribution. A random variable X is said to have a additive Weibull distribution (Lemonte et al [14]) if its pdf is of the form f (x) = (αβxβ−1 + θδxδ−1)e−(αxβ+θxδ), x > 0, α > 0, θ > 0 and δ, β > 0. The relation in (5) will be exploited in this paper to derive some recurrence relations for the moments of k-th upper record values from the additive Weibull distribution and to give a characterization of this distribution
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