Showing papers on "Probability-generating function published in 1969"
22 citations
TL;DR: In this paper, the authors use Gurland's definition and notation for generalized distributions, i.e., given random variables X i with probability generating functions g i (s ), i = 1, 2, 3, if g 3 (s) = g 1 [ g 2 ( s )], they say that X 3 is X 1 generalized by X 2 and write X 3 ~ X 1 V X 2.
Abstract: We use Gurland's (1957) definition and notation for generalized distributions, i.e., given random variables X i with probability generating functions g i ( s ) , i = 1, 2, 3, if g 3 ( s ) = g 1 [ g 2 ( s )], we say that X 3 is X 1 generalized by X 2 and write X 3 ~ X 1 V X 2 .
12 citations
TL;DR: In this article, the authors considered a discrete time Markov chain whose state space is the nonnegative integers and whose transition probability matrix possesses the representation of a sequence of non-negative real numbers satisfying, and a corresponding sequence of probability generating functions.
Abstract: Consider a discrete time Markov chain { Z n } whose state space is the non-negative integers and whose transition probability matrix ║ P ij ║ possesses the representation
where { P r }, r = 1,2,…, is a finite or denumerably infinite sequence of non-negative real numbers satisfying , and , is a corresponding sequence of probability generating functions. It is assumed that Z 0 = k , a finite positive integer.
10 citations
TL;DR: In this paper, the Moran-Gould model of seasonal inflows is used to examine the number of failures n in N years of reservoir operation, and the distribution of failures is derived from the m-step transition matrices (m = 1, 2, N) and the vector of probabilities of intrayear failure corresponding to all states of the system.
Abstract: The distribution of the number of failures n in N years of reservoir operation is examined via the Moran-Gould model of seasonal inflows. This distribution is conditional on the initial state of the system. It is derived from the m-step transition matrices (m = 1, 2, … N) and the vector of probabilities of intrayear failure corresponding to all states of the system Ei (i = 0, 1, 2,… k). Introduction of probability generating functions simplifies the presentation of the material. These functions are briefly discussed. A simple numerical example illustrates the theory.
4 citations
TL;DR: The general form of the characteristic function (c.f.) of a homogeneous random process or, as it is today mostly called, a process with independent and stationary increments is stated.
Abstract: d1. In his famous paper [4] Kohnogoroff has stated—under very general conditions—the general form of the characteristic function (c.f.) of a homogeneous random process or, as it is today mostly called, a process with independent and stationary increments.
2 citations
01 Jun 1969
TL;DR: Distribution function determination using moment generating function and probability density function using moment generator and moment generator is described in this article, where the distribution function is determined using moment generators and moment generators.
Abstract: Distribution function determination using moment generating function and probability density function
1 citations
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TL;DR: In general, when a logical element fails it can fail not only at true or false levels but at any one of infinitely many different voltage levels, thus, strictly speaking, one should talk of probability density function, rather than discrete probabilities.
Abstract: In general, when a logical element fails it can fail not only at true or false levels but at any one of infinitely many different voltage levels. Thus, strictly speaking, one should talk of probability density function, rather than discrete probabilities. When considering the simultaneous failures of several modules one has to consider the joint probability density function.