Moments of kth Lower Record Values from Inverse-Rayleigh Distribution and Characterization

Abstract

This paper focuses on the inverse Rayleigh distribution, a widely used model for lifetime data. We derive expressions for the moments of k^th lower record values and establish recursive relations between these moments. Moreover, we present characterization results based on these recursive relations and conditional moments. We also compute key statistical properties, including mean, variance, skewness, kurtosis, and product moments. Finally, we demonstrate the application of a characterization theorem using both simulated data from this distribution and a real data set.

Keywords: Lower record values; Single moment; Product moments; Inverse Rayleigh distribution; Characterization.

2010 Mathematics Subject Classification. 62G30; 62E10; 60E05