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1
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A model for proportions with medical applications

100%
Nadarajah S.
Applicationes Mathematicae
|
2007
|
tom 34
|
nr 1
15-27
EN
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.
2
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On the use of difference of two proportions

100%
Nadarajah S.
Applicationes Mathematicae
|
2009
|
tom 36
|
nr 4
441-452
EN
Differences of two proportions occur most frequently in biomedical research. However, as far as published work is concerned, only approximations have been used to study the distribution of such differences. In this note, we derive the exact probability distribution of the difference of two proportions for seven flexible beta type distributions. The expressions involve several well known special functions. The use of these results with respect to known approximations is illustrated.
3
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On the ratio of gamma and Rayleigh random variables

100%
Nadarajah S.
Applicationes Mathematicae
|
2007
|
tom 34
|
nr 3
373-382
EN
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.
4
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Asymptotic covariances for the generalized gamma distribution

64%
Withers C., Nadarajah S.
Applicationes Mathematicae
|
2011
|
tom 38
|
nr 1
85-92
EN
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.
5
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A multimodal beta distribution with application to economic data

64%
Nadarajah S., Kotz S.
Applicationes Mathematicae
|
2007
|
tom 34
|
nr 1
1-14
EN
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.
6
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Drought models based on Burr XII variables

64%
Nadarajah S., Kibria B.
Applicationes Mathematicae
|
2006
|
tom 33
|
nr 2
185-193
EN
Burr distributions are some of the most versatile distributions in statistics. In this paper, a drought application is described by deriving the exact distributions of U = XY and W = X/(X+Y) when X and Y are independent Burr XII random variables. Drought data from the State of Nebraska are used.
7
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On the product of triangular random variables

51%
Garg M., Choudhary S., Nadarajah S.
Applicationes Mathematicae
|
2009
|
tom 36
|
nr 4
419-439
EN
We derive the probability density function (pdf) for the product of three independent triangular random variables. It involves consideration of various cases and subcases. We obtain the pdf for one subcase and present the remaining cases in tabular form. We also indicate how to calculate the pdf for the product of n triangular random variables.
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