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1.
Ying-Chao Hung 《Journal of statistical planning and inference》2012,142(1):86-94
We consider the bandit problem with an infinite number of Bernoulli arms, of which the unknown parameters are assumed to be i.i.d. random variables with a common distribution F. Our goal is to construct optimal strategies of choosing “arms” so that the expected long-run failure rate is minimized. We first review a class of strategies and establish their asymptotic properties when F is known. Based on the results, we propose a new strategy and prove that it is asymptotically optimal when F is unknown. Finally, we show that the proposed strategy performs well for a number of simulation scenarios. 相似文献
2.
Order statistics from trivariate normal and -distributions in terms of generalized skew-normal and skew- distributions 总被引:1,自引:0,他引:1
We consider here a generalization of the skew-normal distribution, GSN(λ1,λ2,ρ), defined through a standard bivariate normal distribution with correlation ρ, which is a special case of the unified multivariate skew-normal distribution studied recently by Arellano-Valle and Azzalini [2006. On the unification of families of skew-normal distributions. Scand. J. Statist. 33, 561–574]. We then present some simple and useful properties of this distribution and also derive its moment generating function in an explicit form. Next, we show that distributions of order statistics from the trivariate normal distribution are mixtures of these generalized skew-normal distributions; thence, using the established properties of the generalized skew-normal distribution, we derive the moment generating functions of order statistics, and also present expressions for means and variances of these order statistics.Next, we introduce a generalized skew-tν distribution, which is a special case of the unified multivariate skew-elliptical distribution presented by Arellano-Valle and Azzalini [2006. On the unification of families of skew-normal distributions. Scand. J. Statist. 33, 561–574] and is in fact a three-parameter generalization of Azzalini and Capitanio's [2003. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J. Roy. Statist. Soc. Ser. B 65, 367–389] univariate skew-tν form. We then use the relationship between the generalized skew-normal and skew-tν distributions to discuss some properties of generalized skew-tν as well as distributions of order statistics from bivariate and trivariate tν distributions. We show that these distributions of order statistics are indeed mixtures of generalized skew-tν distributions, and then use this property to derive explicit expressions for means and variances of these order statistics. 相似文献
3.
Kimeldorf et al. (1981) established a simultaneous characterization of the Poisson and Bernoulli distributions. In this note two variants of the authors' characterizing condition are considered each of which is shown also to characterize simultaneously the Poisson and Bernoulli distributions. 相似文献
4.
Manas K. Chattopadhyay 《Statistics》2013,47(3-4):395-402
One of the two independent stochastic processes (or ‘arms’) is selected and observed sequentially at each of n(≤ ∝) stages. Arm 1 yields observations identically distributed with unknown probability measure P with a Dirichlet process prior whereas observations from arm 2 have known probability measure Q. Future observations are discounted and at stage m, the payoff is a m(≥0) times the observation Z m at that stage. The objective is to maximize the total expected payoff. Clayton and Berry (1985) consider this problem when a m equals 1 for m ≤ n and 0 for m > n(< ∝) In this paper, the Clayton and Berry (1985) results are extended to the case of regular discount sequences of horizon n, which may also be infinite. The results are illustrated with numerical examples. In case of geometric discounting, the results apply to a bandit with many independent unknown Dirichlet arms. 相似文献
5.
A. Bazargan-Lari 《Statistical Papers》2004,45(3):433-438
The probability density function of the range R, in random sampling from a uniform distribution on (k, l) and exponential distribution with parameter λ is obtained, when the sample size is a random variable having the Generalized
Polya Eggenberger Distribution of the first kind (GPED
1). The results of Raghunandanan and Patil (1972) and Bazargan-lari (1999) follow as special cases. The p.d.f of rangeR is obtained, when the distribution of the sample sizeN belongs to Katz family of distributions, as a special case.
An erratum to this article is available at . 相似文献
6.
We introduce a new family of skew-normal distributions that contains the skew-normal distributions introduced by Azzalini
(Scand J Stat 12:171–178, 1985), Arellano-Valle et al. (Commun Stat Theory Methods 33(7):1465–1480, 2004), Gupta and Gupta
(Test 13(2):501–524, 2008) and Sharafi and Behboodian (Stat Papers, 49:769–778, 2008). We denote this distribution by GBSN
n
(λ1, λ2). We present some properties of GBSN
n
(λ1, λ2) and derive the moment generating function. Finally, we use two numerical examples to illustrate the practical usefulness
of this distribution. 相似文献
7.
Shahjahan Khan 《Statistical Papers》2009,50(3):511-525
This paper considers multiple regression model with multivariate spherically symmetric errors to determine optimal β-expectation
tolerance regions for the future regression vector (FRV) and future residual sum of squares (FRSS) by using the prediction
distributions of some appropriate functions of future responses. The prediction distribution of the FRV, conditional on the
observed responses, is multivariate Student-t distribution. Similarly, the prediction distribution of the FRSS is a beta distribution. The optimal β-expectation tolerance
regions for the FRV and FRSS have been obtained based on the F -distribution and beta distribution, respectively. The results in this paper are applicable for multiple regression model
with normal and Student-t errors.
相似文献
8.
Divergence measures play an important role in statistical theory, especially in large sample theories of estimation and testing.
The underlying reason is that they are indices of statistical distance between probability distributions P and Q; the smaller
these indices are the harder it is to discriminate between P and Q. Many divergence measures have been proposed since the
publication of the paper of Kullback and Leibler (1951). Renyi (1961) gave the first generalization of Kullback-Leibler divergence,
Jeffreys (1946) defined the J-divergences, Burbea and Rao (1982) introduced the R-divergences, Sharma and Mittal (1977) the
(r,s)-divergences, Csiszar (1967) the ϕ-divergences, Taneja (1989) the generalized J-divergences and the generalized R-divergences
and so on. In order to do a unified study of their statistical properties, here we propose a generalized divergence, called
(h,ϕ)-divergence, which include as particular cases the above mentioned divergence measures. Under different assumptions, it is
shown that the asymptotic distributions of the (h,ϕ)-divergence statistics are either normal or chi square. The chi square and the likelihood ratio test statistics are particular
cases of the (h,ϕ)-divergence test statistics considered. From the previous results, asymptotic distributions of entropy statistics are derived
too. Applications to testing statistical hypothesis in multinomial populations are given. The Pitman and Bahadur efficiencies
of tests of goodness of fit and independence based on these statistics are obtained. To finish, apendices with the asymptotic
variances of many well known divergence and entropy statistics are presented.
The research in this paper was supported in part by DGICYT Grants N. PB91-0387 and N. PB91-0155. Their financial support is
gratefully acknowledged. 相似文献
9.
Gauss M. Cordeiro Antonio Eduardo Gomes Cibele Queiroz da-Silva 《Journal of Statistical Computation and Simulation》2013,83(1):114-138
The Weibull distribution is one of the most important distributions in reliability. For the first time, we introduce the beta exponentiated Weibull distribution which extends recent models by Lee et al. [Beta-Weibull distribution: some properties and applications to censored data, J. Mod. Appl. Statist. Meth. 6 (2007), pp. 173–186] and Barreto-Souza et al. [The beta generalized exponential distribution, J. Statist. Comput. Simul. 80 (2010), pp. 159–172]. The new distribution is an important competitive model to the Weibull, exponentiated exponential, exponentiated Weibull, beta exponential and beta Weibull distributions since it contains all these models as special cases. We demonstrate that the density of the new distribution can be expressed as a linear combination of Weibull densities. We provide the moments and two closed-form expressions for the moment-generating function. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The density of the order statistics can also be expressed as a linear combination of Weibull densities. We obtain the moments of the order statistics. The expected information matrix is derived. We define a log-beta exponentiated Weibull regression model to analyse censored data. The estimation of the parameters is approached by the method of maximum likelihood. The usefulness of the new distribution to analyse positive data is illustrated in two real data sets. 相似文献
10.
Artur J. Lemonte 《Journal of statistical planning and inference》2011,141(5):1981-1989
In this paper we obtain asymptotic expansions up to order n−1/2 for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests. 相似文献
11.
Continuing increases in computing power and availability mean that many maximum likelihood estimation (MLE) problems previously thought intractable or too computationally difficult can now be tackled numerically. However, ML parameter estimation for distributions whose only analytical expression is as quantile functions has received little attention. Numerical MLE procedures for parameters of new families of distributions, the g-and-k and the generalized g-and-h distributions, are presented and investigated here. Simulation studies are included, and the appropriateness of using asymptotic methods examined. Because of the generality of these distributions, the investigations are not only into numerical MLE for these distributions, but are also an initial investigation into the performance and problems for numerical MLE applied to quantile-defined distributions in general. Datasets are also fitted using the procedures here. Results indicate that sample sizes significantly larger than 100 should be used to obtain reliable estimates through maximum likelihood. 相似文献
12.
The number ofl-overlapping success runs of lengthk inn trials, which was introduced and studied recently, is presently reconsidered in the Bernoulli case and two exact formulas
are derived for its probability distribution function in terms of multinomial and binomial coefficients respectively. A recurrence
relation concerning this distribution, as well as its mean, is also obtained. Furthermore, the number ofl-overlapping success runs of lengthk inn Bernoulli trials arranged on a circle is presently considered for the first time and its probability distribution function
and mean are derived. Finally, the latter distribution is related to the first, two open problems regarding limiting distributions
are stated, and numerical illustrations are given in two tables. All results are new and they unify and extend several results
of various authors on binomial and circular binomial distributions of orderk. 相似文献
13.
《统计学通讯:理论与方法》2013,42(11):1899-1912
ABSTRACT An order k (or cluster) generalized Polya distribution and a multivariate generalized Polya-Eggenberger one where derived in (Sen, K.; Jain, R. Cluster Generalized Negative Binomial Distribution. In Probability Models and Statistics, A. J. Medhi Festschrift on the Occasion of his 70th Birthday; Borthakur, A.C. et al., Eds.; New Age International Publishers: New Delhi, 1996; 227–241 and Sen, K.; Jain, R. A Multivariate Generalized Polya-Eggenberger Probability Model-First Passage Approach. Communications in Statistics—Theory and Methods 1997, 26, 871–884). Presently, both distributions are generalized to a multivariate generalized Polya distribution of order k by means of an appropriate sampling scheme and a first passage event. This new distribution includes as special cases new multivariate Polya and inverse Polya distributions of order k and the multivariate generalized negative binomial distribution of the same order derived recently in (Tripsiannis, G.A.; Philippou, A.N.; Papathanasiou, A.A. Multivariate Generalized Distributions of Order k. Medical Statistics Technical Report #41: Democritus University of Thrace, Greece, 2001). Limiting cases are considered and applications are indicated. 相似文献
14.
In the presence of multicollinearity, the r − k class estimator is proposed as an alternative to the ordinary least squares (OLS) estimator which is a general estimator
including the ordinary ridge regression (ORR), the principal components regression (PCR) and the OLS estimators. Comparison
of competing estimators of a parameter in the sense of mean square error (MSE) criterion is of central interest. An alternative
criterion to the MSE criterion is the Pitman’s (1937) closeness (PC) criterion. In this paper, we compare the r − k class estimator to the OLS estimator in terms of PC criterion so that we can get the comparison of the ORR estimator to the
OLS estimator under the PC criterion which was done by Mason et al. (1990) and also the comparison of the PCR estimator to
the OLS estimator by means of the PC criterion which was done by Lin and Wei (2002). 相似文献
15.
A. Bazargan-Lari 《Statistical Papers》2007,48(3):459-466
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 λ is obtained, when the sample size is a random variable from GPED
2. The results of Bazargan-Lari (2004) follow as special cases. 相似文献
16.
Hans Pettersson 《Statistical Papers》2005,46(1):79-99
This paper considers the problem of optimal design for inference in Generalized Linear Models, when prior information about
the parameters is available. The general theory of optimum design usually requires knowledge of the parameter values. These
are usually unknown and optimal design can, therefore, not be used in practice. However, one way to circumvent this problem
is through so-called “optimal design in average”, or shortly, “ave optimal”. The ave optimal design is chosen to minimize
the expected value of some criterion function over a prior distribution. We focus our interest on the aveD
A-optimality, including aveD- and avec-optimality and show the appropriate equivalence theorems for these optimality criterions, which give necessary conditions
for an optimal design. Ave optimal designs are of interest when e.g. a factorial experiment with a binary or a Poisson response
in to be conducted. The results are applied to factorial experiments, including a control group experiment and a 2×2 experiment. 相似文献
17.
In this paper, a discrete counterpart of the general class of continuous beta-G distributions is introduced. A discrete analog of the beta generalized exponential distribution of Barreto-Souza et al. [2], as an important special case of the proposed class, is studied. This new distribution contains some previously known discrete distributions as well as two new models. The hazard rate function of the new model can be increasing, decreasing, bathtub-shaped and upside-down bathtub. Some distributional and moment properties of the new distribution as well as its order statistics are discussed. Estimation of the parameters is illustrated using the maximum likelihood method and, finally, the model with a real data set is examined. 相似文献
18.
In this paper, we discuss a general class of skew two-piece skew-normal distributions, denoted by GSTPSN(λ1, λ2, ρ). We derive its moment generating function and discuss some simple and interesting properties of this distribution. We then
discuss the modes of these distributions and present a useful representation theorem as well. Next, we focus on a different
generalization of the two-piece skew-normal distribution which is a symmetric family of distributions and discuss some of
its properties. Finally, three well-known examples are used to illustrate the practical usefulness of this family of distributions. 相似文献
19.
Minimax Estimation of the Bounded Parameter of Some Discrete Distributions Under LINEX Loss Function
For a class of discrete distributions, including Poisson(θ), Generalized Poisson(θ), Borel(m, θ), etc., we consider minimax estimation of the parameter θ under the assumption it lies in a bounded interval of the form [0, m] and a LINEX loss function. Explicit conditions for the minimax estimator to be Bayes with respect to a boundary supported prior are given. Also for Bernoulli(θ)-distribution, which is not in the mentioned class of discrete distributions, we give conditions for which the Bayes estimator of θ ∈ [0, m], m < 1 with respect to a boundary supported prior is minimax under LINEX loss function. Numerical values are given for the largest values of m for which the corresponding Bayes estimators of θ are minimax. 相似文献
20.
《Journal of Statistical Computation and Simulation》2012,82(7):1015-1021
The Jeffreys-rule prior and the marginal independence Jeffreys prior are recently proposed in Fonseca et al. [Objective Bayesian analysis for the Student-t regression model, Biometrika 95 (2008), pp. 325–333] as objective priors for the Student-t regression model. The authors showed that the priors provide proper posterior distributions and perform favourably in parameter estimation. Motivated by a practical financial risk management application, we compare the performance of the two Jeffreys priors with other priors proposed in the literature in a problem of estimating high quantiles for the Student-t model with unknown degrees of freedom. Through an asymptotic analysis and a simulation study, we show that both Jeffreys priors perform better in using a specific quantile of the Bayesian predictive distribution to approximate the true quantile. 相似文献