The probability generating function of a random variable which has Generalized Polya Eggenberger Distribution of the second kind (GPED(2)) is obtained. The probability density function of the range R, in random sampli...
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The probability generating function of a random variable which has Generalized Polya Eggenberger Distribution of the second kind (GPED(2)) is obtained. The probability density function of the range R, in random sampling from a uniform distribution on (k, l) and exponential distribution with parameter lambda is obtained, when the sample size is a random variable from GPED(2). The results of Bazargan-Lari (2004) follow as special cases.
The Expectation Maximization (EM) algorithm, a popular method for maximum likelihood estimation of parameters, requires a complete data space and construction of a conditional expectation. For many statistical models,...
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The Expectation Maximization (EM) algorithm, a popular method for maximum likelihood estimation of parameters, requires a complete data space and construction of a conditional expectation. For many statistical models, these may not be straightforward. This paper proposes a simpler Alternating Minimization (AM) algorithm using a probability generating function (pgf)-based divergence measure for estimation in univariate and bivariate distributions. The performance of the estimation method is studied for the negative binomial and Neyman Type-A distributions in the univariate setting, while for bivariate cases, the bivariate Poisson and the bivariate negative binomial distributions are considered. Comparison is made with direct optimization of pgf-based divergence measure and maximum likelihood (ML) estimates. Results produced via AM in both simulated and real-life datasets show an improvement in comparison to direct pgf optimization, especially in the bivariate setting, with the execution time showing an improvement for large sample sizes when compared to ML. Goodness-of-fit tests show that the pgf divergence measure with AM estimates mostly perform similarly to the ML estimates in terms of power of the test.
This paper studies properties of parameter estimators obtained by minimizing a distance between the empirical probability generating function and the probability generating function of a model for count data. Specific...
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This paper studies properties of parameter estimators obtained by minimizing a distance between the empirical probability generating function and the probability generating function of a model for count data. Specifically, it is shown that, under certain not restrictive conditions, the resulting estimators are consistent and, suitably normalized, asymptotically normal. These properties hold even if the model is misspecified. Three applications of the obtained results are considered. First, we revisit the goodness-of-fit problem for count data and propose a weighted bootstrap estimator of the null distribution of test statistics based on the above cited distance. Second, we give a probability generating function version of the model selection test problem for separate, overlapping and nested families of distributions. Finally, we provide an application to the problem of testing for separate families of distributions. All applications are illustrated with numerical examples.
We obtain formulas for the probability generating function of general multivariate Bernoulli distributions, and for the moment generatingfunction of the aggregate claim amount for individual risk models with dependen...
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We obtain formulas for the probability generating function of general multivariate Bernoulli distributions, and for the moment generatingfunction of the aggregate claim amount for individual risk models with dependencies. Several examples are given. (c) 2005 Elsevier B.V. All rights reserved.
generatingfunction-based statistical inference is an attractive approach if the probability (density) function is complicated when compared with the generatingfunction. Here, we propose a parameter estimation method...
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generatingfunction-based statistical inference is an attractive approach if the probability (density) function is complicated when compared with the generatingfunction. Here, we propose a parameter estimation method that minimizes a probability generating function (pgf)-based power divergence with a tuning parameter to mitigate the impact of data contamination. The proposed estimator is linked to the M-estimators and hence possesses the properties of consistency and asymptotic normality. In terms of parameter biases and mean squared errors from simulations, the proposed estimation method performs better for smaller value of the tuning parameter as data contamination percentage increases.
In this article, we develop a method to estimate the two parameters of the discrete stable distribution. By minimizing the quadratic distance between transforms of the empirical and theoretical probabilitygenerating ...
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In this article, we develop a method to estimate the two parameters of the discrete stable distribution. By minimizing the quadratic distance between transforms of the empirical and theoretical probability generating functions, we obtain estimators simple to calculate, asymptotically unbiased, and normally distributed. We also derive the expression for their variance-covariance matrix. We simulate several samples of discrete stable distributed datasets with different parameters, to analyze the effect of tuncation on the right tail of the distribution.
Let MO denote the number of empty cells when n distinguishable balls are distributed independently and at random in m cells such that each ball stays with probability p in its cell, and falls through with probability ...
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Characteristics of tactical guarantee network are analyzed,based on which a network model with uniformly random degree distribution and cascade failure survivability model is *** network nodes' initial capacity an...
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Characteristics of tactical guarantee network are analyzed,based on which a network model with uniformly random degree distribution and cascade failure survivability model is *** network nodes' initial capacity and load were equal,the critical point of network cascade collapse is derived by probabilityfunction method *** research shows that:as network load increases, there will be a critical load *** network load exceeds the critical value,a random node failure in the network will cause the entire function network to collapse. Finally,computer simulation is applied to verify the correctness of the analytic deduction.
The use of the probability generating function in testing the fit of dis crete distributions was proposed by Kocherlakota & Kocherlakota (1986), and further studied by Marques and Perez-Abreu (1989). In Rueda et a...
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The use of the probability generating function in testing the fit of dis crete distributions was proposed by Kocherlakota & Kocherlakota (1986), and further studied by Marques and Perez-Abreu (1989). In Rueda et al. (1991), a quadratic statistic to test the fit of a discrete distribution was proposed using the probability generating function and its empirical counterpart. This was illustrated for the Poisson case with known parameter. Here, we deal with some extensions: the Poisson case with unknown parameter and the negative Binomial distribution with known or unknown parameter p. We find the asymptotic distribution of the test statistic in each case, and show with the aid of some Monte Carlo studies the closeness of these asymptotic distributions. A connection is established between this quadratic test and the Cramer von Mises test of fit described in Spinelli (1994) and Spinelli and Stephens (1997), thus providing additional insight into these procedures. Also, a correction is made on the expression of the covariance function of the empirical process as appeared in Rueda et al (1991). Finally, power comparisons are provided for the case of the Poisson test and some examples are given.
Characteristics of tactical guarantee network are analyzed, based on which a network model with uniformly random degree distribution and cascade failure survivability model is proposed. Supposing network nodes' in...
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Characteristics of tactical guarantee network are analyzed, based on which a network model with uniformly random degree distribution and cascade failure survivability model is proposed. Supposing network nodes' initial capacity and load were equal, the critical point of network cascade collapse is derived by probabilityfunction method analysis. The research shows that: as network load increases, there will be a critical load value. When network load exceeds the critical value, a random node failure in the network will cause the entire function network to collapse. Finally, computer simulation is applied to verify the correctness of the analytic deduction.
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