Adding Percentiles of Erlangian Distributions

Numerical Methods for Reliability and Safety Assessment

“…k Á , see Smaili et al (2013a). However, the case when n D 1 the m parameters are identical and the hypoexponential distribution is the Erlang distribution (Anjum and Perros 2011). Written as S m Erl(m,˛i) In the following proposition, we state the PDF, CDF, reliability function, hazard function, MGF, and moment of order k for the Erlang RV, see Abdelkader (2003) and Zukerman (2012).…”

“…In particular the sum of exponential random variable has important applications in the modeling in many domains such as communications and computer science (Trivedi 2002;Anjum and Perros 2011), Markov process (Jasiulewicz and Kordecki 2003;Mathai 1982), insurance (Willmot and Woo 2007;Minkova 2010) and reliability and performance evaluation (Trivedi 2002;Jasiulewicz and Kordecki 2003;Bolch et al 2006;Amari and Misra 1997). Nadarajah (2008) presented a review of some results on the sum of random variables.…”

“…This case was examined by Smaili et al (2013a). However, the case when the parameters are identical the hypoexponential distribution is the Erlang distribution (Anjum and Perros 2011). Also the case when the parameters are distinct, it is known to be the hypoexponential distribution with different parameters discussed by Smaili et al (2013b).…”

Explicit results on conditional distributions of generalized exponential mixtures

“…Convolutions of exponential distributions have been proved to be relevant in various application fields: in management science, [8] provides results on admission scheduling in a clinic with respect to stable bed demand where patient stay lengths follow GEM distributions; in reliability theory, [18] provides bounds for the probability that a system of independent components will operate completely when the component failure probabilities are exponentially distributed with pairwise distinct rates, while [27] derives results on finding the optimal rate of preventive maintenance in Markov systems with GEM time-to-failure distribution; further applications are elaborated by [4] in renewal theory, [9,26] in actuarial science, and [3] in network science; [11] shows how to apply GEMs for approximating arbitrary distribution functions with positive half-line support. Recently, [16] investigated financial risk measures for a system of asymptotically exponentially distributed losses; however, they showed that summation of such losses does not lead to GEM distributions.…”

Hypoexponential Distribution with Different Parameters

“…In particular the sum of exponential random has important applications in the modeling in many domains such as communications and computer science [3,4], Markov process [5,6], insurance [7,8] and reliability and performance evaluation [4,5,9,10]. Nadarajah [11], presented a review of some results on the sum of random variables.…”