Showing papers on "Negative binomial distribution published in 1988"
TL;DR: In this paper, several results for the probability of ruin as well as for the joint distribution of the surpluses immediately before and at ruin were derived for the compound binomial model.
Abstract: The compound binomial model is a discrete time analogue (or approximation) of the compound Poisson model of classical risk theory. In this paper, several results are derived for the probability of ruin as well as for the joint distribution of the surpluses immediately before and at ruin. The starting point of the probabilistic arguments are two series of random variables with a surprisingly simple expectation (Theorem 1) and a more classical result of the theory of random walks (Theorem 2) that is best proved by a martingale argument.
175 citations
TL;DR: In this paper, a simple relation between the parameter k of the negative binomial distribution and the factorial moments (Fi) was proposed to show that there is a significant rise of the Fi with decreasing bin size along the thrust axis.
108 citations
TL;DR: In this article, a different type of binomial distribution of order k is discussed and the mean, the variance and the moment generating function of this distribution are derived, where the mean is defined as the sum of the mean and variance.
101 citations
TL;DR: In this paper, a general recursive relation for the total multiplicity distribution is derived from a random cascading model with intermittency, and conditions for the existence of a fixed point solution are formulated.
68 citations
TL;DR: In this article, the conditional expectation is used to characterize gamma and negative binomial distributions and a necessary and sufficient condition for each distribution is given in terms of the failure rate for each distributions.
Abstract: Characterizations of gamma and negative binomial distributions are presented by using the conditional expectation. A necessary and sufficient condition is given in terms of the failure rate for each distribution. To illustrate the usefulness of the results, the authors discuss the mean residual-life of the gamma distribution. >
43 citations
TL;DR: In this paper, two C(a) statistics for testing the equality of the means of several groups of count data in the presence of a common dispersion parameter are derived, and two applications are given.
Abstract: SUMMARY Two C(a) statistics (Neyman, 1959) for testing the equality of the means of several groups of count data in the presence of a common dispersion parameter are derived. The performance of the two C(a) statistics, the likelihood ratio statistic and two more statistics based on transformed data (Anscombe, 1948) is then compared in terms of size and power by using Monte Carlo simulations. The C(a) statistics are recommended. The C (a) statistics for testing the equality of the dispersion parameters of several groups of count data are also derived. Two applications are given.
42 citations
TL;DR: In this article, an event-based approach adapted to semi-arid climatic conditions and applicable in those cases when only unreliable observation data are available is developed, where emphasis is placed on ease of modeling and computation.
40 citations
TL;DR: In this paper, a model for the claim number process is considered, where the claim process is assumed to be a weighted Poisson process with a three-parameter gamma distribution as the structure function.
Abstract: A model for the claim number process is considered. The claim number process is assumed to be a weighted Poisson process with a three-parameter gamma distribution as the structure function. Fitting of this model to several data encountered in the literature is considered, and the model is compared with the two-parameter gamma model giving the negative binomial distribution. Some credibility theory formulae are also presented.
40 citations
TL;DR: In this paper, the multiplicity distribution for non-single-diffractive π+676p andpp collisions at the collider was studied for full phase space as well as for intervals in rapidity, azimuthal angle and transverse momentum.
Abstract: The charged particle multiplicity distribution has been studied for non-single-diffractive π+
p andpp collisions at
$$\sqrt s = 22$$
GeV, for full phase space as well as for intervals in rapidity, azimuthal angle and transverse momentum. In general, the multiplicity distribution is well described by a negative binomial. From comparison of the distribution for negative or positive particles to that of all charged particles, cascading is favoured as an interpretation over stimulated emission. Interesting consequences follow from a comparison of our results to those at collider energies and toe
+
e
− data at comparable energy. Furthermore, evidence is given that the multiplicity distribution is not exactly of negative binomial type in every (connected or disconnected) phase space region.
35 citations
TL;DR: In this article, a negative binomial distribution of order k is obtained by compounding the extended (or multiparameter) Poisson distribution by the gamma distribution, as the zero truncated limit of the first distribution.
Abstract: A multiparameter negative binomial distribution of order k is obtained by compounding the extended (or multiparameter) Poisson distribution of order k by the gamma distribution. A multiparameter logarithmic series distribution of order k is derived next, as the zero truncated limit of the first distribution. Finally a few genesis schemes and interrelationships are established for these three multiparameter distributions of order k. The present work extends several properties of distributions of order k.
31 citations
01 Nov 1988
TL;DR: A computational method is presented which, when applied to an existing confidence procedure, produces a uniformly superior procedure that produces a family of procedures that constitute a complete class of procedures.
Abstract: April1986 Revised July 1987 Second Revision, March 1988 Third Revision, November 1988 A computational method is presented which, when applied to an existing confidence procedure, produces a uniformly superior procedure. This method, called refinement, actually produces a family of procedures that constitute a complete class. Although details are only given for the Poisson distribution, the refinement process is applicable to any discrete distribution. Tables of refined Poisson confidence intervals are given for confidence levels of .95. An example of refining negative binomial confidence intervals is also included.
TL;DR: In this article, a three-parameter generalisation of the beta-binomial distribution (BBD) derived by Chandon (1976) is examined, and the maximum likelihood estimates of the parameters and the elements of the information matrix are obtained.
Abstract: Summary
A three-parameter generalisation of the beta-binomial distribution (BBD) derived by Chandon (1976) is examined. We obtain the maximum likelihood estimates of the parameters and give the elements of the information matrix. To exhibit the applicability of the generalised distribution we show how it gives an improved fit over the BBD for magazine exposure and consumer purchasing data. Finally we derive an empirical Bayes estimate of a binomial proportion based on the generalised beta distribution used in this study.
TL;DR: Assumptions inherent in use of the binomial distribution are relaxed in order to identify alternative distributions with different variances, for fitting to the frequency distributions of numbers of open channels in multi-channel patches.
TL;DR: A discrete distribution involving Charlier polynomial is considered in this paper, which can be regarded as the counterpart of the non-central negative binomial distribution (Ong and Lee, 1979).
Abstract: A discrete distribution involving Charlier polynomial is considered. This distribution can be regarded as the counterpart of the non-central negative binomial distribution (Ong and Lee, 1979). Application to data-fitting is illustrated.
TL;DR: In this article, the negative binomial and Poisson distributions are fitted to data on scores in Association Football for the seasons 1946-47 to 1983-84, and the analyses are set in the context of previous applications and interpretations in the area.
Abstract: Negative binomial and Poisson distributions are fitted to data on scores in Association Football for the seasons 1946–47 to 1983–84. There are strong grounds for preferring the negative binomial up to 1970; thereafter the Poisson seems adequate. Simplification is achieved by fitting the negative binomial with a common parameter. The analyses are set in the context of previous applications and interpretations in the area. Different models giving rise to the negative binomial or Poisson are investigated and some support found for models not previously advanced in this context. Notwith-standing the success of such exercises some scepticism is expressed about the interpretations placed on previous analyses.
TL;DR: Etude de l'estimation de la moyenne d'une distribution binomiale negative a partir de donnees binomiales correspondant au nombre d'unites d'echantillonnage provenant d'one total donne donné as discussed by the authors.
Abstract: Etude de l'estimation de la moyenne d'une distribution binomiale negative a partir de donnees binomiales correspondant au nombre d'unites d'echantillonnage provenant d'un total donne dont le nombre d'individus est inferieur ou egal a t, nombre determine a priori et application a l'estimation des densites de population des nuisibles en agriculture
TL;DR: In this paper, a distribution which is a long-tailed, unimodal, mixed Poisson extension to the Poisson-Pascal was found to be valid in a larger parameter space.
TL;DR: In this article, a general prior distribution for the binomial parameter n is studied and the assumption of improper priors in both p and n is shown to lead to implausible results.
Abstract: Bayes estimation of the binomial parameter n based on a general prior distribution for n is studied. As special cases improper prior and Poisson prior (which is a natural choice) are considered, and formulae for the marginal and posterior distributions are obtained. It is shown that the assumption of improper priors in both p and n leads to implausible results.
TL;DR: In this paper, the number of distinct prime divisors of binomial coefficients is studied and a numerical result on a conjecture by Erd6s on square divisor is given.
Abstract: This paper, using computational and theoretical methods, deals with prime divisors of binomial coefficients: Geometric distribution and number of distinct prime divisors are studied. We give a numerical result on a conjecture by Erd6s on square divisors of binomial coefficients.
TL;DR: In this article, a simple procedure for estimating the parameters of bivariate discrete distributions is presented, which uses the marginal means and certain observed frequencies in one or more conditional distributions, and asymptotic efficiencies for various parameter values.
Abstract: This paper presents a simple procedure for estimating the parameters of bivariate discrete distributions. The procedure uses the marginal means and certain observed frequencies in one or more conditional distributions. The bivariate Poisson and Negative Binomial distributions are used as illustrative examples, Parameter estimators are derived and asymptotic efficiencies are examined for various parameter values.
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01 Dec 1988TL;DR: In this paper, the authors proposed a bonus-malus system which integrates a priori and a posteriori information on an individual basis, and showed how a multivariate net premium tables can be derived from the model.
Abstract: The objective of this paper is to provide an extension of well-known models of tarification in automobile insurance. The analysis begins by introducing a regression component in the Poisson Model in order to use all available information in the estimation of the distribution. In a second step, a random variable is introduced in the regression component of the Poisson model and a negative binomial model with a regression component is derived. The authors then present their main contribution by proposing a bonus-malus system which integrates a priori and a posteriori information on an individual basis. They then show how a multivariate net premium tables can be derived from the model. Examples of tables are presented. (A)
TL;DR: In this article, a new approach is proposed to evaluate new-product opportunities using the distribution of brand-purchase probability of the new product over a population of potential customers and the outputs from conjoint analysis.
Abstract: A new approach is proposed to evaluate new-product opportunities. This approach uses the distribution of brand-purchase probability of the new product over a population of potential customers and the outputs from conjoint analysis. The heterogeneous distribution of brand-purchase probability is expressed by a beta binomial brand-choice model compounded with a negative binomial product-class purchase-incidence model. The resulting model provides a way to predict trial and repeat-purchase patterns of new-product concepts. The paper discusses the development of the model. It also discusses issues of measurement, estimation, testing, and implementation of the proposed approach based on actual empirical data.
Journal Article•
TL;DR: In this paper, a simple adaptation of the Bates-Neyman model to accident blackspots and estimators of the efficacy of treatment programmes may be devised, using data from the Lothian Road Accident Statistics System (LORASS).
Abstract: This paper considers a simple adaptation of the Bates-Neyman model to accident blackspots and shows how estimators of the efficacy of treatment programmes may be devised. It is shown how the method of maximum likelihood in connection with a bivariate negative binomial distribution may be used to separate treatment effects from regression to the mean effects when analysing data giving the frequency of accidents in two time periods for a number of sites on a road network. The method is illustrated using data from the Lothian Road Accident Statistics System (LORASS).
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TL;DR: In this paper, a study of the finite sample properties of the pseudo-maximum likelihood estimators in the case of a Poisson model is presented, where the simulations have been realized with control variates, a method which has considerably improved the accuracy of the results obtained.
Abstract: This paper presents a study of the finite sample properties of the pseudo-maximum likelihood estimators in the case of a Poisson model. The simulations have been realized with control variates, a method which has considerably improved the accuracy of the results obtained. The negative binomial p. d. f. gives better estimators, for the pseudo-maximum likelihood method, than gamma or normal p. d. f. The quasi-generalized pseudo-maximum likelihood method really improves the results, whichever of those three p. d. f.'s is used.
01 May 1988
TL;DR: In this article, the authors deal with the problem of selecting good negative binomial populations as compared with a standard or a control, and derive the monotone empirical Bayes estimators of the concerned parameters.
Abstract: This paper deals with the problem of selecting good negative binomial populations as compared with a standard or a control. The main results are based on the use of the empirical Bayes approach. First we derive the monotone empirical Bayes estimators of the concerned parameters. Based on these estimators, we construct monotone empirical Bayes selection rules. Asymptotic optimality properties of the monotone empirical Bayes estimators and the monotone empirical Bayes selection rules are investigated. The respective convergence rates for the estimation problem and for the selection problem are studied, under some conditions.
TL;DR: In this article, a distribution function for multiplicity in accordance with the stochastic number evolution is proposed, which gives a universal description of inelastic and non-iffractive multiplicity distributions in pp collisions at 250, 360 and 800 GeV/c.
Abstract: We propose a distribution function for multiplicity in accordance with the stochastic number evolution. This function gives a universal description of inelastic and nondiffractive multiplicity distributions in pp collisions at 250, 360 and 800 GeV/c. The negative binomial distribution fails in the description of inelastic data.
TL;DR: In this paper, a condition on the mixing distribution under which the detection of mixture departures from the Poisson or binomial distribution is detected using a locally most powerful unbiased test is defined.
Abstract: In t h i s note mixture models are used to represent overdispersion relative to Poisson or binomial distributions. We flnd a sufflclent condition on the mixing distribution underich the detection of mixture departures from the Poisson or binomial adrnits a locally most powerful unbiased test. The conditions specify plynoria: relations between the variance and mean of Le glxing distribution.
23 Oct 1988
TL;DR: In this paper, a simple closed-form approximation for the cumulative density function in the case of the straight-line serial search with uniform a priori distribution is derived, based on the exact results.
Abstract: The probability density function of the acquisition time in spread-spectrum serial search initial code acquisition systems has been analyzed, and it was shown that very accurate results can be obtained if the distribution of the partial acquisition times is approximated by the binomial distribution. Furthermore, binomial approximation led to the introduction of the equivalent single-dwell system, i.e., showed that an arbitrary detection/verification scheme can be modeled very well by the simplest single-dwell detection scheme, whose parameters depend only on the mean decision times, and not on their distribution. Based on the exact results, a simple closed-form approximation for the cumulative density function in the case of the straight-line serial search with uniform a priori distribution is derived. >
TL;DR: In this paper, the integral equations for the KNO scaling functions, predicted by QCD in the double logarithmic approximation, for a gluon jet, a quark jet and for a (qq) initial state were solved.
TL;DR: In this article, the use of the binomial distribution for the numerator and the negative binomial for the denominator in prospective studies leads to an unbiased estimate of relative risk and a unbiased estimate for combining experiments.
Abstract: The use of the binomial distribution for the numerator and the negative binomial for the denominator in prospective studies leads to an unbiased estimate of relative risk and an unbiased estimate for combining experiments. Optimal sample sizes for groups are calculated and confidence intervals for the relative risk are presented. The efficiency of plans are evaluated by comparing variances and coefficients of variation.