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Ateeq, Kahkashan; Qasim, Tahira Bano; Alvi, Ayesha Rehman

An extension of Rayleigh distribution and applications. (English) Zbl 1428.62070

Cogent Math. Stat. 6, Article ID 1622191, 17 p. (2019).
Summary: In this article, we have derived a new distribution named as Rayleigh-Rayleigh distribution (RRD) motivated by the transformed transformer technique by A. Alzaatreh et al. [Metron 71, No. 1, 63–79 (2013; Zbl 1302.62026)]. The statistical properties of RRD, comprising of explicit expressions for quantile function, moments, moment generating function, mean deviation, skewness, kurtosis, reliability measures, measures of uncertainty, distributions of order statistics and L moments have been derived. Parameter estimation is carried out using method of maximum-likelihood estimation and Fisher information matrix is derived. The flexibility of the new distribution is assessed by applying it to four real data sets. The comparative behavior of RRD with Rayleigh distribution, Generalized Rayleigh distribution, Exponentiated Rayleigh distribution, Weibull Rayleigh distribution and Alpha Power Rayleigh distribution provided the evidence that it outperforms the other competing distributions.

Cited in 4 Documents

MSC:

62E15 Exact distribution theory in statistics
62F10 Point estimation
62N05 Reliability and life testing
60E05 Probability distributions: general theory

Keywords:

Fisher information matrix; moment generating function; order statistics; maximum-likelihood estimation

Citations:

Zbl 1302.62026

Software:

LMOMENTS
Cite Review PDF
Full Text: DOI
OA License

References:

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