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121.
P.C. Consul 《统计学通讯:理论与方法》2013,42(11):3241-3255
The probability distribution of the total number of games to ruin in a gambler's ruin random walk with initial position n, the probability distribution of the total size of an epidemic starting with n cases and the probability distribution of the number of customers served during a busy period M/M/1 when the service starts with n waiting customers are identical. All these can be easily obtained by using Lagrangian expansions instead of long combinatorial methods. The binomial, trinomial, quadrinomial and polynomial random walks of a particle have been considered with an absorbing barrier at 0 when the particle starts its walks from a point n, and the pgfs. and the probability distributions of the total number of jumps (trials) before absorption at 0 have been obtained. The values for the mean and variance of such walks have also been given. 相似文献
122.
This paper reviews recent developments in the stochastic comparison of order statistics. The results discussed are basically: (l) Stochastic comparisons of linear combinations of order statistics from distributions F and G where G?1 F is convex or starshaped. (2) Stochastic comparisons of individual order statistics and of vectors of order statistics from underlying heterogeneous distributions by the use of majorization and Schur function theory. (3) Stochastic comparison of random processes. Applications to reliability problems are presented illustrating the use and value of the theoretical results described 相似文献
123.
A pivotal quantity for a capture-recapture model is introduced and used to construct an asymptotic confidence region for (ε,N), where ε is the capture efficiency and N is the population size. The true confidence levels of certain regions are obtained by simulation. Certain confidence regions for (ε,N) are drawn to show the size of the regions and to show how confidence limits for N depend on ε. 相似文献
124.
Continuing the studies of Johnson et al (1980) and Johnson and Kotz (1981), further distributions arising from models of errors in inspection and grading of samples from finite, possibly stratified lots are obtained. Screening, and hierarchal screening forms of inspection are also considered, and the effects of errors on the advantages of these techniques assessed. 相似文献
125.
Yongtao Guan Roland Fleißner Paul Joyce Stephen M. Krone 《Statistics and Computing》2006,16(2):193-202
As the number of applications for Markov Chain Monte Carlo (MCMC) grows, the power of these methods as well as their shortcomings
become more apparent. While MCMC yields an almost automatic way to sample a space according to some distribution, its implementations
often fall short of this task as they may lead to chains which converge too slowly or get trapped within one mode of a multi-modal
space. Moreover, it may be difficult to determine if a chain is only sampling a certain area of the space or if it has indeed
reached stationarity.
In this paper, we show how a simple modification of the proposal mechanism results in faster convergence of the chain and
helps to circumvent the problems described above. This mechanism, which is based on an idea from the field of “small-world”
networks, amounts to adding occasional “wild” proposals to any local proposal scheme. We demonstrate through both theory and
extensive simulations, that these new proposal distributions can greatly outperform the traditional local proposals when it
comes to exploring complex heterogenous spaces and multi-modal distributions. Our method can easily be applied to most, if
not all, problems involving MCMC and unlike many other remedies which improve the performance of MCMC it preserves the simplicity
of the underlying algorithm. 相似文献
126.
Many sufficient conditions for inequalities about the mean, median, mode and skewness have been obtained. The paper presents a theorem that unifies already known results, gives some counter-examples, and considers the cases of Pearson distributions. 相似文献
127.
Adam W. Kolkiewicz 《Revue canadienne de statistique》2003,31(3):329-347
The author shows how to find M‐estimators of location whose generating function is monotone and which are optimal or close to optimal. It is easy to identify a consistent sequence of estimators in this class. In addition, it contains simple and efficient approximations in cases where the likelihood function is difficult to obtain. In some neighbourhoods of the normal distribution, the loss of efficiency due to the approximation is quite small. Optimal monotone M‐estimators can also be determined in cases when the underlying distribution is known only up to a certain neighbourhood. The author considers the e‐contamination model and an extension thereof that allows the distributions to be arbitrary outside compact intervals. His results also have implications for distributions with monotone score functions. The author illustrates his methodology using Student and stable distributions. 相似文献
128.
The likelihood-ratio test statistic for testing homogeneity of exponential means with an ordered alternative has a rather complex null distribution. Expressions for the mean and variance of its null distribution are derived, and the accuracy of a two-moment chi-squared approximation is studied. The coefficients needed to implement the approximation are tabled. The application of these results in testing for a constant versus a nondecreasing intensity in a nonhomogeneous Poisson process is also discussed. 相似文献
129.
In this article we provide saddlepoint approximations for some important models of circular data. The particularity of these saddlepoint approximations is that they do not require solving the saddlepoint equation iteratively, so their evaluation is immediate. We first give very accurate approximations to P-values, critical values and power functions for some optimal tests regarding the concentration parameter under wrapped symmetric α-stable and circular normal models. Then, we consider an approximation to the distribution of a projection of the two-dimensional Pearson random walk with exponential step sizes. 相似文献
130.
Saralees Nadarjah 《Allgemeines Statistisches Archiv》2006,90(3):403-418
Summary The exact distributions of the productXY are derived whenX andY are independent random variables and come from the extreme value distribution of Type I, the extreme value distribution of
Type II or the extreme value distribution of Type III. Of the, six possible combinations, only three yield closed-form expressions
for the distribution ofXY. A detailed application of the results is provided to drought data from Nebraska.
The author would like to thank the referees and the Associate Editor for carefully reading the paper and for their great help
in improving the paper. 相似文献