Abstract
In this paper, we use the concept of dual generalized order statistics dgos which was given by Pawlas and Syznal (2001). By using this, we obtain the various theorems and some relations through ratio and inverse moment by using exponentiated-Weibull distribution. Cases for order statistics and lower record values are also considered. Further, we characterize the exponentiated-Weibull distribution through three different methods by using the results obtained in this paper.
Highlights
The exponentiated Weibull distribution was proposed by Mudholkar and Hutson (1996)
Pawlas and Syznal (2001) introduced the concept of lower generalized order statistics lgos which enables have an idea about reverse order statistics and lower record values
We mainly focus on the study of dgos arising from the exponentiated Weibull distribution
Summary
The exponentiated Weibull distribution was proposed by Mudholkar and Hutson (1996). For more distributional properties of the exponentiated Weibull distribution, we may refer to Mudholkar, Srivastava and Freimer (1995) and Nassar and Eissa (2003). A random variable X is said to have exponentiated Weibull distribution (Mudholkar and Hutson (1996)) if its probability density function ( pdf ) is of the form f (x) = x −1 (1 − e− x ) −1e− x , x 0 , , 0. It shows many characteristics quite similar to exponential; Weibull and exponentiated exponential distributions and their df and the pdf are found to have closed forms. The relation in (6) will be used to derive some simple recurrence relations for the moments of dgos from the exponentiated Weibull distribution. Putting m = 0 , k = 1 , in (21), we obtain a recurrence relation for single moments of order statistics of the exponentiated Weibull distribution of the form. Setting m = −1 and k 1 in (21), we get a recurrence relation for single moments of lower k record values from exponentiated Weibull distribution in the form of.
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