260 research outputs found
Kumaraswamy-Half-Cauchy Distribution: Characterizations and Related Results
We present various characterizations of a recently introduced distribution (Ghosh 2014), called Kumaraswamy- Half- Cauchy distribution based on: (i) a simple relation between two truncated moments; (ii) truncated moment of certain function of the 1st order statistic; (iii) truncated moment of certain function of the random variable; (iv) hazard function; (v) distribution of the 1st order statistic; (vi) via record values. We also provide some remarks on bivariate Gumbel copula distribution whose marginal distributions are Kumaraswamy- Half-Cauchy distributions
A new family of unit-distributions: definition, properties and applications
In this study, a new family of unit-distributions is introduced. Then, a unitGumbel distribution, member of the proposed family of unit-distributions, is obtained as an example, and some of its statistical properties are provided. The maximum likelihood method is used for estimating the shape parameter of the unit-Gumbel distribution. In addition, a new family of continuous distributions is defining by using the composition technique. Finally, real data sets are used for modeling purposes. The result shows that the unit-Gumbel distribution is preferable over some well-known unit-distributions such as the beta, Kumaraswamy, and Topp-Leone, and also the unit-Gompertz distribution, which is recently introduced.Publisher's Versio
Kumaraswamy-Half-Cauchy Distribution: Characterizations and Related Results
We present various characterizations of a recently introduced distribution (Ghosh 2014), called Kumaraswamy- Half- Cauchy distribution based on: (i) a simple relation between two truncated moments; (ii) truncated moment of certain function of the 1st order statistic; (iii) truncated moment of certain function of the random variable; (iv) hazard function; (v) distribution of the 1st order statistic; (vi) via record values. We also provide some remarks on bivariate Gumbel copula distribution whose marginal distributions are Kumaraswamy- Half-Cauchy distributions
Another Generalized Transmuted Family of Distributions: Properties and Applications
We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Another generalized transmuted family of distributions. We present some special models. We investigate the asymptotes and shapes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating functions, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and Renyi entropies and order statistics, which hold for any baseline model, certain characterisations are presented. Further, we introduce a bivariate extensions of the new family. We discuss the dierent method of estimation of the model parameters and illustrate the potentiality of the family by means of two applications to real data. A brief simulation for evaluating Maximum likelihood estimator is done
Reparameterizing the Birkhoff Polytope for Variational Permutation Inference
Many matching, tracking, sorting, and ranking problems require probabilistic
reasoning about possible permutations, a set that grows factorially with
dimension. Combinatorial optimization algorithms may enable efficient point
estimation, but fully Bayesian inference poses a severe challenge in this
high-dimensional, discrete space. To surmount this challenge, we start with the
usual step of relaxing a discrete set (here, of permutation matrices) to its
convex hull, which here is the Birkhoff polytope: the set of all
doubly-stochastic matrices. We then introduce two novel transformations: first,
an invertible and differentiable stick-breaking procedure that maps
unconstrained space to the Birkhoff polytope; second, a map that rounds points
toward the vertices of the polytope. Both transformations include a temperature
parameter that, in the limit, concentrates the densities on permutation
matrices. We then exploit these transformations and reparameterization
gradients to introduce variational inference over permutation matrices, and we
demonstrate its utility in a series of experiments
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