Shape measures for the generalized beta exponential distribution

Abstract This paper contains parametric and informational shape measures for various families of the generalized beta exponential distribution since it is important to determination of the distribution shape for analysing an experimental data set. A logistic parameter is used to select independent types of beta exponential distributions, that it allows to combine the distributions of different subfamilies. In this paper the use of parametric shape measures to pre-define distribution shape is discusses. In particular, the initial and standard central moments for the main types of generalized beta exponential distribution are given. In the paper it is proposes to use the entropy coefficient of unshifted distribution as an independent information measure of the shape of unshifted generalized beta exponential distributions. In order to increase the reliability of the preliminary determination of the shape of the model, expressions for the entropy coefficient of shifted families both the generalized beta exponential distributions of the first and second types, and the generalized gamma exponential distribution were obtained. For practical applied the entropy coefficients of unshifted distributions for various subfamilies of generalized beta exponential distributions can be useful.

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Measures of shape for the generalized beta exponential distribution

Journal of Physics Conference Series ◽

10.1088/1742-6596/2094/2/022064 ◽

2021 ◽

Vol 2094 (2) ◽

pp. 022064

Author(s):

V G Polosin

Keyword(s):

Experimental Data ◽

Exponential Distribution ◽

Information Measure ◽

Exponential Distributions ◽

Data Set ◽

Central Moments ◽

Generalized Gamma ◽

Distribution Shape ◽

Independent Information

Abstract This paper contains parametric and informational measures of shape for various families of the generalized beta exponential distribution since it is important to determination of the distribution shape for analysing an experimental data set. A logistic parameter is used to select independent types of beta exponential distributions, that it allows to combine the distributions of different subfamilies. In this paper the use of parametric shape measures to predefine distribution shape is discusses. In particular, the initial and standard central moments for the main types of generalized beta exponential distribution are given. In the paper it is proposes to use the entropy coefficient of unshifted distribution as an independent information measure of the shape of unshifted generalized beta exponential distributions. In order to increase the reliability of the preliminary determination of the shape of the model, expressions for the entropy coefficient of shifted families both the generalized beta exponential distributions of the first and second types, and the generalized gamma exponential distribution were obtained. For practical applied the entropy coefficients of unshifted distributions for various subfamilies of generalized beta exponential distributions can be useful.

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Univariate and bivariate extensions of the generalized exponential distributions

Mathematica Slovaca ◽

10.1515/ms-2021-0073 ◽

2021 ◽

Vol 71 (6) ◽

pp. 1581-1598

Author(s):

Vahid Nekoukhou ◽

Ashkan Khalifeh ◽

Hamid Bidram

Keyword(s):

Em Algorithm ◽

Exponential Distribution ◽

Bivariate Distribution ◽

Generalized Exponential Distribution ◽

Exponential Distributions ◽

Unknown Parameters ◽

Data Set ◽

New Class ◽

Special Cases ◽

Univariate Distribution

Abstract The main aim of this paper is to introduce a new class of continuous generalized exponential distributions, both for the univariate and bivariate cases. This new class of distributions contains some newly developed distributions as special cases, such as the univariate and also bivariate geometric generalized exponential distribution and the exponential-discrete generalized exponential distribution. Several properties of the proposed univariate and bivariate distributions, and their physical interpretations, are investigated. The univariate distribution has four parameters, whereas the bivariate distribution has five parameters. We propose to use an EM algorithm to estimate the unknown parameters. According to extensive simulation studies, we see that the effectiveness of the proposed algorithm, and the performance is quite satisfactory. A bivariate data set is analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice.

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A SIMPLE TEST FOR HIDDEN PERIODICITY IN TIME SERIES DATA

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127495000211 ◽

1995 ◽

Vol 05 (01) ◽

pp. 265-269 ◽

Cited By ~ 1

Author(s):

MICHAEL ROSENBLUM ◽

JÜRGEN KURTHS

Keyword(s):

Experimental Data ◽

Time Series ◽

Spectral Analysis ◽

Additive Noise ◽

Time Series Data ◽

Series Data ◽

Simple Test ◽

Data Set ◽

Dynamical Characteristics

We would like to draw the attention of specialists in time series analysis to a simple but efficient algorithm for the determination of hidden periodic regimes in complex time series. The algorithm is stable towards additive noise and allows one to detect periodicity even if the examined data set contains only a few periods. In such cases it is more suitable than other techniques, such as spectral analysis or recurrence map. We recommend the use of this test prior to the evaluation of attractor dimensions and other dynamical characteristics from experimental data.

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