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31.
The known methods for computing percentage points of multivariate t distributions are reviewed. We believe that this review will serve as an important reference and encourage further research activities in the area. 相似文献
32.
Saralees Nadarajah 《Quality and Quantity》2009,43(6):993-998
Pareto optimality (sometimes known as Pareto efficiency) is an important notion in social sciences and related areas, see
e.g. Klaus (2006), Chun (2005), Hild (2004), Kibris (2003), Nandeibam (2003), Papai (2001), Peris and Sanchez (2001), Brams
and Fishburn (2000), Denicolo (1999), Klaus et al. (1998), Peremans et al. (1997), and Vohra (1992). This notion invariably
involves the comparison of the utility of one outcome versus another, i.e. the ratio of two utilities or in general the ratio
of two random variables. In this note, we derive the exact distribution of the ratio X/(X + Y) when X and Y are Pareto random variables, Pareto distribution being the first and the most popular distribution used in social sciences
and related areas. 相似文献
33.
In recent years, several composite models based on the lognormal distribution have been developed for the Danish fire insurance data. In this note, we propose new composite models based on the lognormal distribution. At least one of the newly proposed models is shown to give a better fit to the Danish fire insurance data. 相似文献
34.
We give the cumulative distribution function of M n , the maximum of a sequence of n observations from an autoregressive process of order 1. Solutions are first given in terms of repeated integrals and then for the case, where the underlying random variables are absolutely continuous. When the correlation is positive, $$P \left( M_n \leq x \right)\ =a_{n,x},$$ where $$a_{n,x}= \sum_{j=1}^\infty \beta_{jx}\ \nu_{jx}^{n} = O \left( \nu_{1x}^{n}\right),$$ where {?? jx } are the eigenvalues of a non-symmetric Fredholm kernel, and ?? 1x is the eigenvalue of maximum magnitude. When the correlation is negative $$P \left( M_n \leq x \right)\ =a_{n,x} +a_{n-1,x}.$$ The weights ?? jx depend on the jth left and right eigenfunctions of the kernel. These are given formally by left and right eigenvectors of an infinite Toeplitz matrix whose eigenvalues are just {?? jx }. These results are large deviations expansions for extremes, since the maximum need not be standardized to have a limit. In fact, such a limit need not exist. The use of the derived expansion for P(M n ?? x) is illustrated using both simulated and real data sets. 相似文献
35.
Beta distributions are popular models for economic data. In this paper, six new distributions are introduced which generalize the standard beta distribution. These distributions involve the trigonometric functions, sine and cosine. Expressions are derived for their analytical shapes, nth moments, method of moments estimators, maximum likelihood estimators and the associated Fisher information matrices. These calculations involve several special functions. A numerical study is performed to show the flexility of these distributions as compared to the standard beta distribution. An application to consumer expenditure data is illustrated to show that the proposed distributions are better models to economic data than one based on the standard beta distribution. Possible ways of extending the models are also discussed. 相似文献
36.
Two methods are given for adapting a kernel density estimate to obtain an estimate of a density function with bias O(h p ) for any given p, where h = h(n) is the bandwidth and n is the sample size. The first method is standard. The second method is new and involves use of Bell polynomials. The second method is shown to yield smaller biases and smaller mean squared errors than classical kernel density estimates and those due to Jones et al. (Biometrika 82:327–338, 1995). 相似文献
37.
Cusum charts are widely used for detecting deviations of a process about a target value and also for finding evidence of change in the mean of a process. The testing theory approximates the process by a Wiener process or a Brownian bridge, respectively. For quality control, it is important that other aspects are monitored in addition to or instead of the mean. Here, we show that cusum theory is easily adapted when the target is not the mean but some other aspect of the distribution. 相似文献
38.
Analytical bias reduction methods are developed for univariate rounded data for the first time. Extensions are given to rounding of multivariate data, and to smooth functionals of several distributions. As a by‐product, we give for the first time the relation between rounded and unrounded multivariate cumulants. Estimators obtained by analytical bias reduction are compared with bootstrap and jackknife estimators by simulation. 相似文献
39.
The known sampling distributions and simulation methods associated with multivariate t distributions are reviewed. We believe that this review will serve as an important reference and encourage further research activities in the area. 相似文献
40.
Saralees Nadarajah 《Quality and Quantity》2009,43(5):855-863
The failure rate function is an important quantity characterizing life phenomena. Ideally, one would expect this function
to exhibit a bathtub shape. In this paper, a comprehensive review of the known distributions that exhibit this shape is provided.
Over 17 such distributions are identified. This review is especially important because almost all of the commonly known distributions
in statistics do not exhibit the bathtub shape. Furthermore, it could serve as an important reference and encourage developments
of further distributions that exhibit a bathtub shape. 相似文献