scholarly journals One-Parameter Weibull-Type Distribution, Its Relative Entropy with Respect to Weibull and a Fractional Two-Parameter Exponential Distribution

Stats ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 34-54
Author(s):  
Aris Alexopoulos
Keyword(s):  
Exponential Distribution ◽  
Relative Entropy ◽  
Real Data ◽  
Parameter Distribution ◽  
Sample Mean ◽  
Type Distribution ◽  
Two Parameter ◽  
New Distribution ◽  
Extra Parameter ◽  
Mathematical Characteristics

A new one-parameter distribution is presented with similar mathematical characteristics to the two parameter conventional Weibull. It has an estimator that only depends on the sample mean. The relative entropy with respect to the Weibull distribution is derived in order to examine the level of similarity between them. The performance of the new distribution is compared to the Weibull and in some cases the Gamma distribution using real data. In addition, the Exponential distribution is modified to include an extra parameter via a simple transformation using fractional mathematics. It will be shown that the modified version also exhibits Weibull characteristics for particular values of the second parameter.

scholarly journals On Erlang-Truncated Exponential Distribution: Theory and Application

2021 ◽  
pp. 155-168
Author(s):  
Ibrahim Elbatal ◽  
A. Aldukeel
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Mean Deviation ◽  
Model Parameters ◽  
Data Sets ◽  
Survival Times ◽  
New Distribution ◽  
Better Than

In this article, we introduce a new distribution called the McDonald Erlangtruncated exponential distribution. Various structural properties including explicit expressions for the moments, moment generating function, mean deviation of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated by two real data sets. The new model is much better than other important competitive models in modeling relief times and survival times data sets.

scholarly journals An extensive extension of exponentiated exponential distribution using alpha power transformation – statistical properties and applications in engineering science

2021 ◽  
Vol 17 (2) ◽  
pp. 59-74
Author(s):  
S. Qurat Ul Ain ◽  
K. Ul Islam Rather
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Statistical Properties ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model ◽  
Mean Variance ◽  
New Distribution ◽  
Extra Parameter

Abstract In this article, an extension of exponentiated exponential distribution is familiarized by adding an extra parameter to the parent distribution using alpha power technique. The new distribution obtained is referred to as Alpha Power Exponentiated Exponential Distribution. Various statistical properties of the proposed distribution like mean, variance, central and non-central moments, reliability functions and entropies have been derived. Two real life data sets have been applied to check the flexibility of the proposed model. The new density model introduced provides the better fit when compared with other related statistical models.

Comparison of stochastic models of rainfall processes in mountainous climatic conditions

2010 ◽  
Vol 1 (2) ◽  
pp. 135-146
Author(s):  
J. Y. Lee ◽  
M. Y. Han ◽  
D. K. Kim ◽  
W. H. Ji
Keyword(s):  
Exponential Distribution ◽  
Gamma Distribution ◽  
Rainwater Harvesting ◽  
Daily Rainfall ◽  
Percentage Error ◽  
Parameter Distribution ◽  
Mountainous Region ◽  
Simpler Algorithm ◽  
Two Parameter ◽  
Mixed Exponential Distribution

The main objective of this work was to find a stochastic simulation model that was suitable for designing a rainwater harvesting system for agricultural water utilization and irrigation water in a mountainous region. Several models were applied using daily rainfall data from two sites (Gangneung and Daekwanreung) to assess the accuracy and suitability of the model for simulating the daily rainfall. The amount of rainfall for the mountainous region was well described by a two-parameter gamma distribution and performed better than other distributions. However, validation tests revealed that the annual mean absolute percentage error (MAPE) was more than 10% at both locations. This result was different from some previous research in which a three-parameter mixed-exponential distribution was well described. In addition, although the exponential distribution was also well described by a second-order expression, the use of a one-parameter distribution had a simpler algorithm than the two-parameter gamma distribution and the three-parameter mixed-exponential distribution.

scholarly journals The Exponentiated Generalized Standardized Half-logistic Distribution

2017 ◽  
Vol 6 (3) ◽  
pp. 24 ◽  
Author(s):  
Gauss M. Cordeiro ◽  
Thiago A. N. De Andrade ◽  
Marcelo Bourguignon ◽  
Frank Gomes-Silva
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Data Set ◽  
Lorenz Curves ◽  
Lifetime Model ◽  
Two Parameter ◽  
New Distribution

We study a new two-parameter lifetime model called the exponentiated generalized standardized half-logistic distribution, which extends the half-logistic pioneered by Balakrishnan in the eighties. We provide explicit expressions for the moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves, and order statistics. The model parameters are estimated by the maximum likelihood method. A simulation study reveals that the estimators have desirable properties such as small biases and variances even in moderate sample sizes. We prove empirically that the new distribution provides a better fit to a real data set than other competitive models.

scholarly journals The Exponential-Generalized Truncated Geometric (EGTG) Distribution: A New Lifetime Distribution

2017 ◽  
Vol 7 (1) ◽  
pp. 1 ◽  
Author(s):  
Mohieddine Rahmouni ◽  
Ayman Orabi
Keyword(s):  
Probability Distribution ◽  
Real Data ◽  
Lifetime Distribution ◽  
Data Sets ◽  
Application Study ◽  
Maximum Lifetime ◽  
Special Cases ◽  
Rate Functions ◽  
Two Parameter ◽  
New Distribution

This paper introduces a new two-parameter lifetime distribution, called the exponential-generalized truncated geometric (EGTG) distribution, by compounding the exponential with the generalized truncated geometric distributions. The new distribution involves two important known distributions, i.e., the exponential-geometric (Adamidis and Loukas, 1998) and the extended (complementary) exponential-geometric distributions (Adamidis et al., 2005; Louzada et al., 2011) in the minimum and maximum lifetime cases, respectively. General forms of the probability distribution, the survival and the failure rate functions as well as their properties are presented for some special cases. The application study is illustrated based on two real data sets.

scholarly journals A New Version of the Exponentiated Exponential Distribution: Copula, Properties and Application to Relief and Survival Times

2021 ◽  
Vol 9 (2) ◽  
pp. 311-333
Author(s):  
Hanaa Elgohari
Keyword(s):  
Exponential Distribution ◽  
Hazard Function ◽  
Real Data ◽  
Likelihood Method ◽  
Type Model ◽  
Data Sets ◽  
Survival Times ◽  
Mathematical Properties ◽  
Mean Variance ◽  
New Distribution

In this paper, we introduce a new generalization of the Exponentiated Exponential distribution. Various structural mathematical properties are derived. Numerical analysis for mean, variance, skewness and kurtosis and the dispersion index is performed. The new density can be right skewed and symmetric with "unimodal" and "bimodal" shapes. The new hazard function can be "constant", "decreasing", "increasing", "increasing-constant", "upside down-constant", "decreasing nstant". Many bivariate and multivariate type model have been also derived. We assess the performance of the maximum likelihood method graphically via the biases and mean squared errors. The usefulness and flexibility of the new distribution is illustrated by means of two real data sets.

scholarly journals A New Extension of Lindley Geometric Distribution and its Applications

2019 ◽  
pp. 249-263
Author(s):  
I. Elbatal ◽  
Mohamed G. Khalil
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Geometric Distribution ◽  
Real Data ◽  
Rate Function ◽  
Likelihood Method ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Data Set ◽  
New Distribution

A new four-parameter distribution called the beta Lindley-geometric distribution is proposed. The hazard rate function of the new model can be constant, decreasing, increasing, upside down bathtub or bathtub failure rate shapes. Various structural properties including of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated using a real data set.

scholarly journals The Topp-Leone Generated Weibull Distribution: Regression Model, Characterizations and Applications

2016 ◽  
Vol 6 (1) ◽  
pp. 126 ◽  
Author(s):  
Gokarna R. Aryal ◽  
Edwin M. Ortega ◽  
G. G. Hamedani ◽  
Haitham M. Yousof
Keyword(s):  
Weibull Distribution ◽  
Regression Model ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Lifetime Model ◽  
First Time ◽  
Two Parameter ◽  
New Distribution

This paper introduces a new four-parameter lifetime model called the Topp Leone Generated Weibull (TLGW) distribution. This distribution is a generalization of the two parameter Weibull distribution using the genesis of Topp-Leone distribution.  We derive many of its structural properties including ordinary and incomplete moments, quantile and generating functions and order statistics. Parameter estimation using maximum likelihood method and simulation results to assess effectiveness of the distribution are discussed. Also, for the first time, we introduce a regression model based on the new distribution. We prove empirically the importance and flexibility of the new model in modeling various types of real data sets.

scholarly journals A Gamma-Type Distribution with Applications

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 870 ◽  
Author(s):  
Yuri A. Iriarte ◽  
Héctor Varela ◽  
Héctor J. Gómez ◽  
Héctor W. Gómez
Keyword(s):  
Real Data ◽  
Random Variable ◽  
Independent Random Variables ◽  
Parameter Distribution ◽  
Ml Estimation ◽  
Type Distribution ◽  
Generalized Gamma ◽  
Positive Data ◽  
Identifiability Problem ◽  
Different Levels

This article introduces a new probability distribution capable of modeling positive data that present different levels of asymmetry and high levels of kurtosis. A slashed quasi-gamma random variable is defined as the quotient of independent random variables, a generalized gamma is the numerator, and a power of a standard uniform variable is the denominator. The result is a new three-parameter distribution (scale, shape, and kurtosis) that does not present the identifiability problem presented by the generalized gamma distribution. Maximum likelihood (ML) estimation is implemented for parameter estimation. The results of two real data applications revealed a good performance in real settings.

scholarly journals A New Modified Kies Family: Properties, Estimation Under Complete and Type-II Censored Samples, and Engineering Applications

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1345 ◽  
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Mohammed K. Shakhatreh ◽  
Mazen Nassar ◽  
Ahmed Z. Afify
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Real Data ◽  
Mean Residual Life ◽  
Type Ii ◽  
Censored Samples ◽  
New Family ◽  
Generalized Distributions ◽  
Two Parameters ◽  
New Distribution

In this paper, we introduce a new family of continuous distributions that is called the modified Kies family of distributions. The main mathematical properties of the new family are derived. A special case of the new family has been considered in more detail; namely, the two parameters modified Kies exponential distribution with bathtub shape, decreasing and increasing failure rate function. The importance of the new distribution comes from its ability in modeling positively and negatively skewed real data over some generalized distributions with more than two parameters. The shape behavior of the hazard rate and the mean residual life functions of the modified Kies exponential distribution are discussed. We use the method of maximum likelihood to estimate the distribution parameters based on complete and type-II censored samples. The approximate confidence intervals are also obtained under the two schemes. A simulation study is conducted and two real data sets from the engineering field are analyzed to show the flexibility of the new distribution in modeling real life data.

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