Abstract
The distribution of a linear combination of random variables arise in many applied problems, and have been extensively studied by different researchers. This article derived the exact distribution of the linear combination aX + bY , where a > 0 and b are real constants, and X and Y denote gamma and Rayleigh random variables respectively and are distributed independently of each other. The associated cdfs and pdfs have been derived. The plots for the cdf and pdf, percentile points for selected coefficients and parameters, and the statistical application of the results have been provided. We hope thefindings of the paper will be useful for practitioners in various fields.
Highlights
The distributions of the linear combination of two independent random variables arise in many fields of research, see, for example, Ladekarl et al (1997), Amari and Misra (1997), Cigizoglu and Bayazit (2000), Galambos and Simonelli (2005), Nadarajah and Kibria (2006a, 2006b), among others
There has been a great interest in the study of the distributions of the linear combination a X + b Y, when X and Y are independent random variables and belong to different families, among them, Nadarajah and Kotz (2005) for the linear combination of exponential and gamma random variables, Kibria and Nadarajah (2007) for the linear combination of exponential and Rayleigh random variables, and Nason (2006) for the distributions of the sum X + Y, when X and Y are independent normal and sphered student’s t random variables respectively, are notable
This paper discusses the distributions of the linear combination aX + bY, when
Summary
The distributions of the linear combination of two independent random variables arise in many fields of research, see, for example, Ladekarl et al (1997), Amari and Misra (1997), Cigizoglu and Bayazit (2000), Galambos and Simonelli (2005), Nadarajah and Kibria (2006a, 2006b), among others. This paper discusses the distributions of the linear combination aX + bY , when. The derivations of the associated cdf’s and pdf’s in this paper involve some special functions, which are defined as follows. It is well-known that, for Re(p) > 0, and Re(α) > 0,.
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