Joint distributions of random variables and their integrals for certain birth-death and diffusion processes
| Autor: | J. Gani, D. R. Mcneil |
|---|---|
| Rok vydání: | 1971 |
| Předmět: |
Statistics and Probability
Multivariate random variable Applied Mathematics 010102 general mathematics Statistical parameter Algebra of random variables 01 natural sciences 010104 statistics & probability Joint probability distribution Sum of normally distributed random variables Statistical physics Diffusion (business) Marginal distribution 0101 mathematics Random variable Mathematics |
| Zdroj: | Advances in Applied Probability. 3:339-352 |
| ISSN: | 1475-6064 0001-8678 |
| DOI: | 10.1017/s0001867800037988 |
| Popis: | For the linear growth birth-death process with parameters λ n = nλ, μ n = nμ, Puri ((1966), (1968)) has investigated the joint distribution of the number X(t) of survivors in the process and the associated integral Y(t) = ∫0 t X(τ)dτ. In particular, he has obtained limiting results as t → ∞. Recently one of us (McNeil (1970)) has derived the distribution of the integral functional W x = ∫0 Tx g{X(τ)}dτ, where T x is the first passage time to the origin in a general birth-death process with X(0) = x and g(·) is an arbitrary function. Functionals of the form W x arise naturally in traffic and storage theory; for example W x may represent the total cost of a traffic jam, or the cost of storing a commodity until expiration of the stock. Moments of such functionals were found in the case of M/G/1 and GI/M/1 queues by Gaver (1969) and Daley (1969). |
| Databáze: | OpenAIRE |
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