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4 Applicationes Mathematicae

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On the ratio of gamma and Rayleigh random variables

100%

Nadarajah S.

nr 3

373-382

The gamma and Rayleigh distributions are two of the most applied distributions in engineering. Motivated by engineering issues, the exact distribution of the quotient X/Y is derived when X and Y are independent gamma and Rayleigh random variables. Tabulations of the associated percentage points and a computer program for generating them are also given.

A model for proportions with medical applications

100%

Nadarajah S.

nr 1

15-27

Data that are proportions arise most frequently in biomedical research. In this paper, the exact distributions of R = X + Y and W = X/(X+Y) and the corresponding moment properties are derived when X and Y are proportions and arise from the most flexible bivariate beta distribution known to date. The associated estimation procedures are developed. Finally, two medical data sets are used to illustrate possible applications.

Asymptotic covariances for the generalized gamma distribution

63%

Withers C. , Nadarajah S.

nr 1

85-92

The five-parameter generalized gamma distribution is one of the most flexible distributions in statistics. In this note, for the first time, we provide asymptotic covariances for the parameters using both the method of maximum likelihood and the method of moments.

A multimodal beta distribution with application to economic data

63%

Nadarajah S. , Kotz S.

nr 1

1-14

Beta distributions are popular models for economic data. In this paper, a new multimodal beta distribution with bathtub shaped failure rate function is introduced. Various structural properties of this distribution are derived, including its cdf, moments, mean deviation about the mean, mean deviation about the median, entropy, asymptotic distribution of the extreme order statistics, maximum likelihood estimates and the Fisher information matrix. Finally, an application to consumer price indices is illustrated to show that the proposed distribution is a better model to economic data than one based on the standard beta distribution.