REPUBLIC OF SERBIA

MINISTRY OF DEFENCE

www.mod.gov.rs

MINISTRY OF DEFENCE

Material Resources Sector

Defensive Technologies Department

Military Technical Institute

www.vti.mod.gov.rs

Statistics of ratio of two weibull random variables with different parameters

ivica marjanović

Republic of Serbia Ministry of Defence, Belgrade, ivicabeograd@gmail.com

DEjan rančić

Faculty of Electronic Engineering, University of Niš, Niš, dejan.rancic@elfak.ni.ac.rs

danijela aleksić

College of Applied Technical Sciences, University of Niš, Niš, danijela.aleksic@vtsnis.edu.rs

dejan milić

Faculty of Electronic Engineering, University of Niš, Niš, dejan.mailic@elfak.ni.ac.rs

mihajlo stefanović

Faculty of Electronic Engineering, University of Niš, Niš, misa.profesor@gmail.com

Abstract: In this paper the ratio of two Weibull random variables with different parameters is considered. Probability density function and cumulative distribution function of proposed ratio are evaluated. Derived expression for probability density function can be used for evaluation bit error probability and the expression for cumulative distribution function can be used for calculation outage probability of wireless communication radio system operating over Weibull short term fading channel in the presence of co-channel interference subjected to Weibull fading. The influence of Weibull non linearity parameters and average powers of Weibull fading on outage probability is analysed.

Keywords: Weibull fading, random variable, probability density function (PDF), cumulative distribution function (CDF), level crossing rate (LCR).