Skellam reference manual (original) (raw)
Related papers
A Retrospective Study on Skellam and Related Distributions
Austrian Journal of Statistics, 2022
This paper reviews works on Skellam distribution, its extensions and areas of applications. Available literature shows that this distribution is flexible for modelling integer data where they appear as count data or paired count data in the field of finance, medicine, sports, and science. Bivariate Skellam distribution, dynamic Skellam model and other extensions are also discussed and additional literature are provided.
On the bivariate Skellam distribution
Communications in Statistics - Theory and Methods, 2015
In this paper, we introduce a new distribution on Z 2 , which can be viewed as a natural bivariate extension of the Skellam distribution. The main feature of this distribution a possible dependence of the univariate components, both following univariate Skellam distributions. We explore various properties of the distribution and investigate the estimation of the unknown parameters via the method of moments and maximum likelihood. In the experimental section, we illustrate our theory. First, we compare the performance of the estimators by means of a simulation study. In the second part, we present two applications to a real data set and show how an improved fit can be achieved by estimating mixture distributions.
Precise tabulation of the maximally-skewed stable distributions and densities
Computational Statistics & Data Analysis, 1997
The cdf and pdf of the maximally skewed (/~ = 1) stable distributions are tabulated to high precision, by means of Zolotarev's integral representation, for ct = 0.50 (0.02) 2.00, at fractiles corresponding to p = 0.0001, 0.001, 0.005, 0.01 (0.01) 0.99, 0.995, 0.999, 0.9999. This tabulation is intended to be suitable for developing and calibrating a numerical approximation to these distributions. The probability at the tabulated fractiles is estimated to be accurate to within 4.1 × 10-~o. The densities have an absolute precision of 2.0 x 10-13 and a relative precision of 1.6 x 10-12. Zolotarev's correction of the discontinuity at ct = 1 is graphically illustrated. The full tabulation, documented here, is available by anonymous FTP.
This manuscript illustrates the implementation and testing of nine statistical distributions, namely Beta, Binomial, Chi-Square, F, Gamma, Geometric, Poisson, Student's t and Uniform distribution, where each distribution consists of three common functions-Probability Density Function (PDF), Cumulative Density Function (CDF) and the inverse of CDF (inverseCDF).
The Kummer Beta Normal: A New Useful-Skew Model
Journal of data science: JDS
The normal distribution is the most popular model in applications to real data. We propose a new extension of this distribution, called the Kummer beta normal distribution, which presents greater flexibility to model scenarios involving skewed data. The new probability density function can be represented as a linear combination of exponentiated normal pdfs. We also propose analytical expressions for some mathematical quantities: Ordinary and incomplete moments, mean deviations and order statistics. The estimation of parameters is approached by the method of maximum likelihood and Bayesian analysis. Likelihood ratio statistics and formal goodness-of-fit tests are used to compare the proposed distribution with some of its sub-models and non-nested models. A real data set is used to illustrate the importance of the proposed model.
2015
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Journal of Statistical Sciences
Statistical Science
CITATIONS 0 READS 40 2 authors: Some of the authors of this publication are also working on these related projects: statistical shape clustering , Msc. thesis View project A Study on Skew Circular Distributions, Msc. thesis View project
Objective Bayesian Analysis of Skew-tDistributions
Scandinavian Journal of Statistics, 2012
We study the Jeffreys prior and its properties for the shape parameter of univariate skew-t distributions with linear and nonlinear Student's t skewing functions. In both cases, we show that the resulting priors for the shape parameter are symmetric around zero and proper. Moreover, we propose a Student's t approximation of the Jeffreys prior that makes an objective Bayesian analysis easy to perform. We carry out a Monte Carlo simulation study that demonstrates an overall better behaviour of the maximum a posteriori estimator compared with the maximum likelihood estimator. We also compare the frequentist coverage of the credible intervals based on the Jeffreys prior and its approximation and show that they are similar. We further discuss location-scale models under scale mixtures of skew-normal distributions and show some conditions for the existence of the posterior distribution and its moments. Finally, we present three numerical examples to illustrate the implications of our results on inference for skew-t distributions.
A class of skewed distributions with applications in environmental data
Communications in Statistics: Case Studies, Data Analysis and Applications, 2019
In environmental studies, many data are typically skewed and it is desired to have a flexible statistical model for this kind of data. In this paper, we study a class of skewed distributions by invoking arguments as described by Ferreira and Steel (2006, Journal of the American Statistical Association, 101: 823-829). In particular, we consider using the logistic kernel to derive a class of univariate distribution called the truncated-logistic skew symmetric (TLSS) distribution. We provide some structural properties of the proposed distribution and develop the statistical inference for the TLSS distribution. A simulation study is conducted to investigate the efficacy of the maximum likelihood method. For illustrative purposes, two real data sets from environmental studies are used to exhibit the applicability of such a model.