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31.
AbstractMotivated by a recent article published by Adam and Tawn, we characterize the distribution of two random variables X, Y ordered linearly like X < Y. We suppose that the random variables follow a bivariate extreme value distribution. 相似文献
32.
ABSTRACTThe gamma distribution has been widely used in many research areas such as engineering and survival analysis. We present an extension of this distribution, called the Kummer beta gamma distribution, having greater flexibility to model scenarios involving skewed data. We derive analytical expressions for some mathematical quantities. The estimation of parameters is approached by the maximum likelihood method and Bayesian analysis. The likelihood ratio and formal goodness-of-fit tests are used to compare the presented distribution with some of its sub-models and non nested models. A real data set is used to illustrate the importance of the distribution. 相似文献
33.
The Kumaraswamy Gumbel distribution 总被引:1,自引:0,他引:1
Gauss M. Cordeiro Saralees Nadarajah Edwin M. M. Ortega 《Statistical Methods and Applications》2012,21(2):139-168
The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. We propose
a generalization—referred to as the Kumaraswamy Gumbel distribution—and provide a comprehensive treatment of its structural
properties. We obtain the analytical shapes of the density and hazard rate functions. We calculate explicit expressions for
the moments and generating function. The variation of the skewness and kurtosis measures is examined and the asymptotic distribution
of the extreme values is investigated. Explicit expressions are also derived for the moments of order statistics. The methods
of maximum likelihood and parametric bootstrap and a Bayesian procedure are proposed for estimating the model parameters.
We obtain the expected information matrix. An application of the new model to a real dataset illustrates the potentiality
of the proposed model. Two bivariate generalizations of the model are proposed. 相似文献
34.
The distribution of linear combinations of random variables arises explicitly in many areas of engineering. This has increased the need to have available the widest possible range of statistical results on linear combinations of random variables. In this note, the exact distribution of the linear combination α X+β Y is derived when X and Y are Laplace and logistic random variables distributed independently of each other. Extensive tabulations of the associated percentage points obtained by inverting the derived distribution are also given. 相似文献
35.
Ricardo Rocha Saralees Nadarajah Vera Tomazella Francisco Louzada 《Lifetime data analysis》2016,22(2):216-240
The presence of immune elements (generating a fraction of cure) in survival data is common. These cases are usually modeled by the standard mixture model. Here, we use an alternative approach based on defective distributions. Defective distributions are characterized by having density functions that integrate to values less than \(1\), when the domain of their parameters is different from the usual one. We use the Marshall–Olkin class of distributions to generalize two existing defective distributions, therefore generating two new defective distributions. We illustrate the distributions using three real data sets. 相似文献
36.
Value at risk and expected shortfall are the two most popular measures of financial risk. But the available R packages for their computation are limited. Here, we introduce an R contributed package written by the authors. It computes the two measures for over 100 parametric distributions, including all commonly known distributions. We expect that the R package could be useful to researchers and to the financial community. 相似文献
37.
Sadegh Rezaei Behnam Bahrami Sadr Morad Alizadeh Saralees Nadarajah 《统计学通讯:理论与方法》2017,46(6):2893-2909
We introduce a new family of distributions based on a one-parameter distribution exhibiting bathtub-shaped hazard rates. We study the mathematical properties of the family and estimate its parameters by the method of maximum likelihood. Finally, the usefulness of the family is illustrated using a real dataset. 相似文献
38.
The distribution of the Liu-type estimator of the biasing parameter in elliptically contoured models
We derive the density function of the stochastic shrinkage parameters of the Liu-type estimator in elliptical models. The correctness of derivation is checked by simulations. A real data application is also provided. 相似文献
39.
The exact distribution of the linear combination α X + β Y is derived when X and Y are normal and logistic random variables distributed independently of each other. Tabulations of the associated percentage
points are given along with a computer program to generate them. This work is motivated by problems in reliability engineering. 相似文献
40.
Saralees Nadarajah 《AStA Advances in Statistical Analysis》2010,94(3):231-246
The important problem of the ratio of Weibull random variables is considered. Two motivating examples from engineering are
discussed. Exact expressions are derived for the probability density function, cumulative distribution function, hazard rate
function, shape characteristics, moments, factorial moments, skewness, kurtosis and percentiles of the ratio. Estimation procedures
by the methods of moments and maximum likelihood are provided. The performances of the estimates from these methods are compared
by simulation. Finally, an application is discussed for aspect and performance ratios of systems. 相似文献