THE RECURRENCE RELATIONS OF ORDER STATISTICS MOMENTS FOR POWER LOMAX DISTRIBUTION

Abstract

The power Lomax distribution due to Rady et al. (2016) is an alternative to and provides
better fits for bladder cancer data (Lee and Wang, 2003) than the Lomax, exponential Lomax,
Weibull Lomax, extended Poisson Lomax and beta Lomax distributions. Exact explicit
expressions as well as recurrence relations for the single and double (product) moments
have been derived from the power Lomax distribution. These recurrence relations
enable computation of the mean, variance, skewness and kurtosis of all order statistics for
all sample sizes in a simple and efficient manner. By using these relation, the mean, variance,
skewness and kurtosis of order statistics for sample sizes up to 5 for various values of
shape and scale parameters are tabulated. Finally, remission times (in months) of bladder
cancer patients have been analyzed to show how the proposed relations work in practice.