Showing papers on "Probability mass function published in 1997"

About distances of discrete distributions satisfying the data processing theorem of information theory

Abstract: The distances of discrete probability distributions are considered. Necessary and sufficient conditions for validity of the data processing theorem of information theory are established. These conditions are applied to the Burbea-Rao (1982) divergences and Bregman (1967) distances.

Introduction To Probability And Statistics for Scientists and Engineers

Abstract: 1 Data Analysis2 Probability Theory3 Discrete Random Variables and their Distribution Functions4 Continuous Random Variables and their Distribution Functions5 Multivariate Probability Distributions6 Sampling Distribution Theory7 Point and Interval Estimation8 Inferences about Population Means9 Inferences about Population Proportions10 Linear Regression and Correlation11 Multiple Linear Regression12 Single Factor Experiments: Analysis of Variance13 Design and Analysis of Multifactor Experiments14 Statistical Quality ControlAppendix A: TablesAnswers to Odd-Numbered Problems

A probabilistic approach to robust control

Abstract: Considers a probabilistic approach to robust control. We construct explicitly the probability density function for the associated distribution of a random sample set of the robust performance index function which itself is a function of a vector of random variables. Using this probability density function, we derive several bounds on the minimum sample size required to estimate a robust performance index function with prescribed probability and confidence. These bounds show that the probabilistic approach to the robust control analysis and synthesis based on this framework has low complexity. Furthermore, a way of constructing the distribution function of the performance index function is proposed which gives the tradeoff between the performance and the risk.

Probabilistic Scaling for the Numerical Inversion of Nonprobability Transforms

Abstract: It is known that probability density functions and probability mass functions usually can be calculated quite easily by numerically inverting their transforms (Laplace transforms and generating functions, respectively) with the Fourier-series method. Other more general functions can be substantially more difficult to invert, because the aliasing and roundoff errors tend to be more difficult to control. In this article we propose a simple new scaling procedure for nonprobability functions that is based on transforming the given function into a probability density function or a probability mass function and transforming the point of inversion to the mean. This new scaling is even useful for probability functions, because it enables us to compute very small values at large arguments with controlled relative error.

Probability and information

Abstract: Probability and information , Probability and information , کتابخانه دیجیتال جندی شاپور اهواز

Efficient estimators for the good family

Abstract: We consider the problem of estimating the two parameters of the discrete Good distribution. We first show that the sufficient statistics for the parameters are the arithmetic and the geometric means. The maximum likelihood estimators (MLE's) of the parameters are obtained by solving numerically a system of equations involving the Lerch zeta function and the sufficient statistics. We find an expression for the asymptotic variance-covariance matrix of the MLE's, which can be evaluated numerically. We show that the probability mass function satisfies a simple recurrence equation linear in the two parameters, and propose the quadratic distance estimator (QDE) which can be computed with an ineratively reweighted least-squares algorithm. the QDE is easy to calculate and admits a simple expression for its asymptotic variance-covariance matrix. We compute this matrix for the MLE's and the QDE for various values of the parameters and see that the QDE has very high asymptotic efficiency. Finally, we present a numer...

A tight upper bound on discrete entropy

Abstract: The standard upper bound on discrete entropy was derived based on the differential entropy bound for continuous random variables. A tighter discrete entropy bound is derived using the transformation formula of Jacobi theta function. The new bound is applicable only when the probability mass function of the discrete random variable satisfies certain conditions. Its application to the class of binomial random variables is presented as an example.

Estimating parameters for discrete distributions via the empirical probability generating function

Abstract: We consider parameter estimation for a family of discrete distributions characterized by probability generating functions (pgf's). Kemp and Kemp (1988) suggest estimators based on the empirical probability generating function (epgf) the methods involve solving estimating equations obtained by equating functionals of the epgf and pgf on a fixed, finite set of values. We derive asymptotic theory for these estimators and consider some examples. Graphical techniques based on the theory are shown to be useful for exploratory analysis

Nonstationary optimal paths and tails of prehistory probability density in multistablestochastic systems

Abstract: The tails of prehistory probability density in nonlinear multistable stochastic systems driven by white Gaussian noise, which has been a subject of recent study, are analyzed by employing the concepts of nonstationary optimal fluctuations. Results of numerical simulations evidence that the prehistory probability density is non-Gaussian and highly asymmetrical that is an essential feature of noise driven fluctuations in nonlinear systems. We show also that in systems with the detail balance the prehistory probability density is the conventional transition probability that obeys the backward Kolmogorov equation.

Demo program for central limit theorem

Abstract: In this paper is described the demo program for the visualization of central limit theorem The program is created for the educational purpose and is implemented in MATLAB Successive sums of the chosen random sequences and the estimations of their probability density functions are displayed In order to compare, the corresponding normal sequence and its probability density function, are also displayed

Extended stirling family of discrete probability distributions

Abstract: In this paper. introduced is a family of discrete probability distributions. whose probability function includes explieitly the Striling-Carlitz polynomial of the first or the second kind. The new family extends the stirling family of distributions. Sibuya (1988) includes the conditional distributions of the orginal ones and enlarges the application area.

A note on the Quasi-Bayesian audit risk model for dollar unit sampling1

Abstract: The Quasi-Bayesian (QB) model generates a complete probability mass function on the total amount of error in an accounting population for any random sample of dollar units or physical units. This probability mass function is used to estimate upper bounds (UBs) on the total amount of error in an accounting population. The underlying QB formulation can be summarized as Bayes' Theorem with a maximum likelihood, calculated using the multinomial distribution, substituted for the unknown likelihood. Any prior can be used. McCray did not provide any theoretical justification for using a maximum likelihood. To date the justification for the QB estimated UBs rests on intuitive arguments limited simulations and ‘windtunnel’ tests. All these suggest the QB UBs may be reliable for audit purposes. This paper provides the theoretical justification for using a maximum likelihood in the QB model. It is based on the concept of ‘partial prior information’.

Genericity and Randomness over Feasible Probability Measures.

Abstract: This paper investigates the notion of resource-bounded genericity developed by Ambos-Spies, Fleischhack, and Huwig. Ambos-Spies, Neis, and Terwijn have recently shown that every language that is t(n)-random over the uniform probability measure is t(n)-generic. It is shown here that, in fact, every language that is t(n)-random over any strongly positive, t(n)-computable probability measure is t(n)-generic. Roughly speaking, this implies that, when genericity is used to prove a resource-bounded measure result, the result is not specific to the underlying probability measure.

Likelihood analyses of overdispersed poisson models

Abstract: written here as LAGPS[O, A], the resulting estimated predictive probability mass functions being shown in Scollnik's Figure 3. The first set of priors was gamma[2, 0.25] for 0, where the gamma[oa, d] distribution has density O3xK-c. exp(-3x)/F(o), and uniform[O, 1] for A. The second set had the same gamma distribution for 0, and for A it had the probability density {exp(0.5[1-(1-A)-2])}/(1A)3, corresponding to a negative exponential distribution with rate 0.5 for the (index of dispersion 1). The mass functions are remarkably similar, raising the question as to how different the results for standard maximum likelihood (ML) would be. (Janardan, Kerster, and Schaeffer [1979] fitted these data using moments, obtaining an excellent fit.) The social behavior of the isopods would plausibly lead to a deficiency in the single-bug class and a corresponding inflation of the other classes. Perhaps the simplest model for this is obtained by taking a basic Poisson[A] distribution, applying a factor of w to the unit class, and scaling all others by the corresponding factor to produce a probability distribution (abbreviated as PS1[w, A]). (Cole [1946] had proposed some rather more complicated ad hoc models.) These two models, LAGPS and PSI, when fitted by ML (all the non-Bayesian fits described below use ML) to the quoted data give results shown in the third and fourth columns of Table 1. The fit for LAGPS[0, A] is obviously very good, with a chi-squared value of 13.4 with 13 d.f. (grouping to at least unity from the smallest class upwards, if necessary repeatedly) and a P-value of 0.41. (A negative binomial fit is very similar.) The PS1[w, A] fit is equally obviously very bad (chi-squared of 386 with 7 d.f.), so that this simplest model is not acceptable; moreover, the estimate of w, the factor by which the unit class is supposed to be reduced is 2.5, with a standard error of 0.6, which is not at all consistent with the model in context. The alternative, very similar model for which all the transferred probability from the unit class is placed in the zero class fits almost as badly. For LAGPS, comparisons of the ML estimates with the two sets of Bayesian procedure estimates are shown in Table 2 (extracted from Scollnik's Figure 3), using the headings of Mean and SD for

A branch-and-bound method for finding independently distributed probability models that satisfy probability order constraints

Abstract: A branch-and-bound method for finding independently distributed probability models is presented. Such models attempt to capture expert preference by (inequality) order relationships and are useful for the development of decision support systems. Finding probability models with independent distributions can be formulated as a linear-constraint optimization problem with a dynamic cost function. A simplex-like algorithm was implemented for branching and bounding between two search spaces on finding the desired models. In these two search spaces, one encompasses all possible independent probability distributions, while the other encompasses all distributions that satisfy all probability order constraints.

On maximal number of probability measures on finite set separated in L/sub 1/ metrics

Abstract: A new upper bound for the maximal number of pairwise separated in metrics L/sub 1/ probability measures on a finite alphabet is obtained.

Fréchet Classes and Nonmonotone Dependence

Abstract: The analysis of the Frechet class of bivariate distribution functions with fixed marginals is fundamental in the study of positive dependence. Several notions of positive dependence have been examined in the literature (see (1982), Kimeldorf and Sampson (1987, Kimeldorf and Sampson 1989), and (1996) for surveys of the field). All of these notions tend to capture the idea that, for a certain random pair, large values of one random variable go together with large values of the other random variable. Another way of expressing this concept is to say that the distribution of the random pair tends to concentrate its mass around the graph of an increasing function. The stronger the dependence, the more concentrated the probability mass will be around the graph of the function. If the marginal distributions are continuous, in the extreme case of a perfect positive dependence all the mass will lie exactly on the graph of an increasing function. Since the marginals are fixed, there exists only one increasing function on whose graph the probability mass can concentrate.

Statistical Properties of Transition Amplitudes in Generic Systems

Abstract: I review some recent results on the statistical properties of matrix elements of typical observables (transition amplitudes) in an eigenbasis of generic quantum Hamiltonian systems. The classical limit of an underlying system can be either integrable, or fully chaotic, or mixed with regular and irregular regions coexisting in phase space. In any case, the variance of transition amplitudes (the local average transition probability) as a function of energy and transition frequency can be calculated in terms of classical power spectra. The probability distribution of transition amplitudes in high energy (semiclassical) regime is derived by means of random matrix theory, whereas in low and intermediate energy (nonsemiclassical) regime the probability distribution of transition amplitudes exhibits universal exponential tails which still call for theoretical explanation.

Probability density function of the line-of-sight angle error

Abstract: The closed form probability density function (PDF) of the angle between the input and output of the time discrete AWGN channel is derived. Two N-dimensional Cartesian systems are considered. The PDF can be used for calculation of the corresponding cumulative distribution function (CDF) which determines the best known general lower and upper bounds on the decoding error probability of optimal block codes on the AWGN channel. For odd values of N/spl ges/3 this reduces to a closed form too.