On the Characteristics and Application of Inverse Power Pranav Distribution

In this article, we study the mathematical characteristics of the inverse power Pranav distribution. The proposed distribution has three special cases namely Pranav, inverse Pranav and inverse power Pranav distributions. In addition with the basic properties of the distribution, the maximum likelihood method was employed in computing the parameters of the distribution. The 95% confidence interval was estimated for each of the parameters and finally, the distribution was applied to 128 bladder cancer patients to illustrate its applicability, and compared to Pranav distribution, inverse power Lindley distribution and inverse Ishita distribution. However, the inverse power Pranav distribution proved superiority over the competing models.

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The Weibull-Gamma Distribution: Properties and Applications

Entropy ◽

10.3390/e21050438 ◽

2019 ◽

Vol 21 (5) ◽

pp. 438 ◽

Cited By ~ 2

Author(s):

Hadeel S. Klakattawi

Keyword(s):

Maximum Likelihood ◽

Gamma Distribution ◽

Maximum Likelihood Method ◽

Data Distribution ◽

Likelihood Method ◽

Parameter Distribution ◽

Great Flexibility ◽

Special Cases ◽

New Distribution ◽

Family Of Distributions

A new member of the Weibull-generated (Weibull-G) family of distributions—namely the Weibull-gamma distribution—is proposed. This four-parameter distribution can provide great flexibility in modeling different data distribution shapes. Some special cases of the Weibull-gamma distribution are considered. Several properties of the new distribution are studied. The maximum likelihood method is applied to obtain an estimation of the parameters of the Weibull-gamma distribution. The usefulness of the proposed distribution is examined by means of five applications to real datasets.

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POTENTIAL FEATURES OF THE MAXIMUM LIKELIHOOD METHOD

SOFT MEASUREMENTS AND COMPUTING ◽

10.36871/2618-9976.2021.06.004 ◽

2021 ◽

Vol 1 (6) ◽

pp. 28-44

Author(s):

Valery A. Pakhotin ◽

◽

Ksenia V. Vlasova ◽

Roman V. Simonov ◽

Sergey V. Petrov ◽

...

Keyword(s):

Maximum Likelihood ◽

Communication Systems ◽

Maximum Likelihood Method ◽

Spectral Lines ◽

Likelihood Method ◽

Model Calculations ◽

Radio Engineering ◽

Signal Parameters ◽

Special Cases ◽

Statistical Problems

In this paper, the potential possibilities of the maximum likelihood method for solving statistical problems of radio engineering are analyzed. A condition is introduced for the correlation interval of a random vector of parameters of a set of signals, which expands the scope of the maximum likelihood method under conditions of a priori and parametric uncertainty. Proofs are given that the known methods of spectral, correlation analysis, and angular spectral analysis are special cases of the maximum likelihood method. The scope of their application for signal processing is limited. They determine the optimal estimates of the signal parameters only when the adopted implementation contains a single signal. The substantiation of the possibility of obtaining solutions to statistical problems of radio engineering in the field of nonorthogonality of signals, when spectral lines, correlation functions, radiation patterns partially coincide, is given. The issues of solving the problem of separate detection of a set of signals based on the proposed optimal receiver are discussed. The issues of separate estimation of signal parameters in the area of their nonorthogonality are discussed. The conditions of the maximum resolution of signals are analyzed. The possibility of creating maximum likelihood filters based on likelihood equations is discussed. It is shown that such filters allow separating signals in the area of their nonorthogonality. They are the basis for solving the problem of channel sealing in communication systems. They make it possible to develop communication systems with nonorthogonal carrier frequencies. A concrete example shows the possibility of exceeding the speed of information transmission in nonorthogonal communication systems in comparison with the maximum speed, which follows from the Shannon theorem. The paper presents the results of model calculations illustrating the provisions of the theory.

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A Unimodal/Bimodal Skew/Symmetric Distribution Generated from Lambert’s Transformation

Symmetry ◽

10.3390/sym13020269 ◽

2021 ◽

Vol 13 (2) ◽

pp. 269

Author(s):

Yuri A. Iriarte ◽

Mário de Castro ◽

Héctor W. Gómez

Keyword(s):

Parameter Estimation ◽

Maximum Likelihood ◽

Structural Properties ◽

Maximum Likelihood Method ◽

Bimodal Distribution ◽

Symmetric Distribution ◽

Likelihood Method ◽

Simulation Experiments ◽

Special Cases ◽

New Distribution

The generalized bimodal distribution is especially efficient in modeling univariate data exhibiting symmetry and bimodality. However, its performance is poor when the data show important levels of skewness. This article introduces a new unimodal/bimodal distribution capable of modeling different skewness levels. The proposal arises from the recently introduced Lambert transformation when considering a generalized bimodal baseline distribution. The bimodal-normal and generalized bimodal distributions can be derived as special cases of the new distribution. The main structural properties are derived and the parameter estimation is carried out under the maximum likelihood method. The behavior of the estimators is assessed through simulation experiments. Finally, two applications are presented in order to illustrate the utility of the proposed distribution in data modeling in different real settings.

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