The Power Series Exponential Power Series Distributions with Applications to Failure Data Sets

Sankhya B ◽  
2021 ◽  
Author(s):  
Rasool Roozegar ◽  
Saralees Nadarajah ◽  
Eisa Mahmoudi
Keyword(s):  
Power Series ◽  
Data Sets ◽  
Failure Data ◽  
Exponential Power ◽  
Power Series Distributions

A New Class of Beta-Complementary Exponential Power Series Distributions

2018 ◽  
Vol 46 (5) ◽  
pp. 20170036
Author(s):  
E. Mahmoudi ◽  
R. S. Meshkat ◽  
M. Entezari
Keyword(s):  
Power Series ◽  
New Class ◽  
Exponential Power ◽  
Power Series Distributions

Generalized exponential–power series distributions

2012 ◽  
Vol 56 (12) ◽  
pp. 4047-4066 ◽  
Author(s):  
Eisa Mahmoudi ◽  
Ali Akbar Jafari
Keyword(s):  
Power Series ◽  
Exponential Power ◽  
Power Series Distributions

scholarly journals The Exponentiated Burr XII Power Series Distribution: Properties and Applications

Stats ◽  
2018 ◽  
Vol 2 (1) ◽  
pp. 15-31
Author(s):  
Arslan Nasir ◽  
Haitham Yousof ◽  
Farrukh Jamal ◽  
Mustafa Korkmaz
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Power Series ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Model Parameters ◽  
Data Sets ◽  
Power Series Distributions ◽  
New Distribution

In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains several important lifetime models. We derive explicit expressions for the ordinary and incomplete moments and generating functions. We discuss the maximum likelihood estimation of the model parameters. The maximum likelihood estimation procedure is presented. We assess the performance of the maximum likelihood estimators in terms of biases, standard deviations, and mean square of errors by means of two simulation studies. The usefulness of the new model is illustrated by means of three real data sets. The new proposed models provide consistently better fits than other competitive models for these data sets.

scholarly journals A Compound Class of the Inverse Gamma and Power Series Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1328
Author(s):  
Pilar A. Rivera ◽  
Enrique Calderín-Ojeda ◽  
Diego I. Gallardo ◽  
Héctor W. Gómez
Keyword(s):  
Power Series ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Hazard Functions ◽  
New Class ◽  
Inverse Gamma ◽  
Gamma Power ◽  
Power Series Distributions ◽  
Quantile Method

In this paper, the inverse gamma power series (IGPS) class of distributions asymmetric is introduced. This family is obtained by compounding inverse gamma and power series distributions. We present the density, survival and hazard functions, moments and the order statistics of the IGPS. Estimation is first discussed by means of the quantile method. Then, an EM algorithm is implemented to compute the maximum likelihood estimates of the parameters. Moreover, a simulation study is carried out to examine the effectiveness of these estimates. Finally, the performance of the new class is analyzed by means of two asymmetric real data sets.

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

On Certain Properties of Power-Series Distributions

Biometrika ◽  
1959 ◽  
Vol 46 (3/4) ◽  
pp. 486 ◽  
Author(s):  
C. G. Khatri
Keyword(s):  
Power Series ◽  
Power Series Distributions
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