Storage capacity of a dam with gamma type inputs

  title={Storage capacity of a dam with gamma type inputs},
  author={Arak M. Mathai},
  journal={Annals of the Institute of Statistical Mathematics},
  • A. M. Mathai
  • Published 1 December 1982
  • Mathematics
  • Annals of the Institute of Statistical Mathematics
SummaryConsider mutually independent inputsX1,...,Xn onn different occasions into a dam or storage facility. The total input isY=X1+...+Xn. This sum is a basic quantity in many types of stochastic process problems. The distribution ofY and other aspects connected withY are studied by different authors when the inputs are independently and identically distributed exponential or gamma random variables. In this article explicit exact expressions for the density ofY are given whenX1,...,Xn are… Expand
Density and distribution evaluation for convolution of independent gamma variables
The Kummer confluent hypergeometric function is demonstrated to be computationally most efficient and a new computationally efficient formula is derived for the probability mass function of the number of renewals by a given time. Expand
System availability in a gamma alternating renewal process
We measure the effectiveness of a repairable system by the proportion of time the system is on, where on-time and off-times are assumed independent and both gamma-distributed. This measure is helpfulExpand
Convolution of geometrics and a reliability problem
In single-shot expensive tests of a destructive nature, an inverse sampling scheme is often pursued in order to use the available resources efficiently. This is particularly relevant for evaluatingExpand
The Distribution of the Sum of Independent Product of Bernoulli and Exponential
SYNOPTIC ABSTRACT The product of the independent Bernoulli and exponential random variables (rv's), has received great attention in recent literature, in particular because of its applications inExpand
An approximation to the convolution of gamma distributions
  • Marco Barnabani
  • Mathematics, Computer Science
  • Commun. Stat. Simul. Comput.
  • 2017
A general negative binomial distribution is suggested to approximate Moschopoulos’s expression looking for an approximating theoretical discrete distribution for the weights of the series and is an “excellent” approximation, fast and simple to implement for any parameter combination. Expand
Notes on the sum and maximum of independent exponentially distributed random variables with different scale parameters
We consider the distribution of the sum and the maximum of a collection of independent exponentially distributed random variables. The focus is laid on the explicit form of the density functionsExpand
We consider a representation of the probability density func- tion of a weighted convolution of the gamma distribution, where a con- fluent hypergeometric function describes how the differencesExpand
The Distributions of Sums for Shanker, Akash, Ishita, Pranav, Rani, and Ram Awadh
In statistics and probability theory, one of the most important statistics is the sums of random variables. After introducing a probability distribution, determining the sum of n independent andExpand
Stochastic dynamics of BOD in a stream with random inputs
Biochemical oxygen demand (BOD) is one of the key variables used to evaluate the quality of river water and in recent years great efforts have been made to model BOD dynamics in a probabilistic way.Expand
On the distribution of the sum of independent and non-identically extended exponential random variables
Considering the sum of the independent and non-identically distributed random variables is a most important topic in many scientific fields. An extension of the exponential distribution based onExpand


The theory of stochastic processes
This book should be of interest to undergraduate and postgraduate students of probability theory.
Queues and Inventories