scholarly journals Odd Inverse Power Generalized Weibull Generated Family of Distributions: Properties and Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
A.S. Al-Moisheer ◽  
I. Elbatal ◽  
Waleed Almutiry ◽  
Mohammed Elgarhy
Keyword(s):  
Likelihood Estimation ◽  
Exponential Model ◽  
Rate Function ◽  
Least Square ◽  
Inverse Power ◽  
Real World Data ◽  
Least Square Estimation ◽  
New Family ◽  
New Models ◽  
Generated Family

A novel family of produced distributions, odd inverse power generalized Weibull generated distributions, is introduced. Various mathematics structural properties for the odd inverse power generalized Weibull generated family are computed. Numerical analysis for mean, variance, skewness, and kurtosis is performed. The new family contains many new models, and the densities of the new models can be right skewed and symmetric with “unimodal” and “bimodal” shapes. Also, its hazard rate function can be “constant,” “decreasing,” “increasing,” “increasing-constant,” “upside-down-constant,” and “decreasing-constant.” Different types of entropies are calculated. Some numerical values of various entropies for some selected values of parameters for the odd inverse power generalized Weibull exponential model are computed. The maximum likelihood estimation, least square estimation, and weighted least square estimation approaches are used to estimate the OIPGW-G parameters. Many bivariate and multivariate type models have been also derived. Two real-world data sets are used to demonstrate the new family’s use and versatility.

Mathematical properties of the Kumaraswamy-Lindley distribution and its applications

2017 ◽  
Vol 5 (1) ◽  
pp. 17
Author(s):  
Hamdy Salem ◽  
Abd-Elwahab Hagag
Keyword(s):  
Hazard Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Least Square ◽  
Estimation Of Parameters ◽  
Least Square Estimation ◽  
Mathematical Properties ◽  
Composite Distribution

In this paper, a composite distribution of Kumaraswamy and Lindley distributions namely, Kumaraswamy-Lindley Kum-L distribution is introduced and studied. The Kum-L distribution generalizes sub-models for some widely known distributions. Some mathematical properties of the Kum-L such as hazard function, quantile function, moments, moment generating function and order statistics are obtained. Estimation of parameters for the Kum-L using maximum likelihood estimation and least square estimation techniques are provided. To illustrate the usefulness of the proposed distribution, simulation study and real data example are used.

scholarly journals Truncated Inverted Kumaraswamy Generated Family of Distributions with Applications

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1089 ◽  
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Rate Function ◽  
Parametric Models ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Full Generality ◽  
Kumaraswamy Distribution ◽  
New Family ◽  
Generated Family ◽  
Family Of Distributions

In this article, we introduce a new general family of distributions derived to the truncated inverted Kumaraswamy distribution (on the unit interval), called the truncated inverted Kumaraswamy generated family. Among its qualities, it is characterized with tractable functions, has the ability to enhance the flexibility of a given distribution, and demonstrates nice statistical properties, including competitive fits for various kinds of data. A particular focus is given on a special member of the family defined with the exponential distribution as baseline, offering a new three-parameter lifetime distribution. This new distribution has the advantage of having a hazard rate function allowing monotonically increasing, decreasing, and upside-down bathtub shapes. In full generality, important properties of the new family are determined, with an emphasis on the entropy (Rényi and Shannon entropy). The estimation of the model parameters is established by the maximum likelihood method. A numerical simulation study illustrates the nice performance of the obtained estimates. Two practical data sets are then analyzed. We thus prove the potential of the new model in terms of fitting, with favorable results in comparison to other modern parametric models of the literature.

scholarly journals Odd Generalized N-H Generated Family of Distributions with Application to Exponential Model

2020 ◽  
pp. 53-71
Author(s):  
Zubair Ahmad ◽  
M. Elgarhy ◽  
G.G. Hamedani ◽  
Nadeem Shafique Butt
Keyword(s):  
Real Data ◽  
Quantile Function ◽  
Exponential Model ◽  
Mean Deviation ◽  
Parameter Estimates ◽  
Data Sets ◽  
New Family ◽  
Maximum Likelihood Procedure ◽  
Generated Family ◽  
Family Of Distributions

A new family of distributions called the odd generalized N-H is introduced and studied. Four new special models are presented. Some mathematical properties of the odd generalized N-H family are studied. Explicit expressions for the moments, probability weighted, quantile function, mean deviation, order statistics and Rényi entropy are investigated. Characterizations based on the truncated moments, hazard function and conditional expectations are presented for the generated family. Parameter estimates of the family are obtained based on maximum likelihood procedure. Two real data sets are employed to show the usefulness of the new family.

Key Subsystem Identification of the CNC Machine Tools

2013 ◽  
Vol 329 ◽  
pp. 157-162 ◽  
Author(s):  
Xiao Cui Zhu ◽  
Fei Chen ◽  
Xiao Bing Li ◽  
Zhao Jun Yang ◽  
Ying Nan Kan ◽  
...  
Keyword(s):  
Machine Tools ◽  
Probability Function ◽  
Likelihood Estimation ◽  
Least Square ◽  
Cnc Machine Tools ◽  
Cnc Machine ◽  
Least Square Estimation ◽  
Failure Data ◽  
Novel Method

In order to find the key subsystems which affect the reliability of the CNC machine tools is an important and yet harder problem due to the lack of failure data and statistical analysis. A novel method based on posterior probability function for identifying the key subsystems of the CNC machine tools was proposed. Firstly, subsystem reliability of the CNC machine tools was estimated using the John estimator, since the failure data were censored. Secondly, parametric fitting was conduct with Weibull distribution using the maximum likelihood estimation (MLE) or the least square estimation (LSE). Thirdly, the probability function of each subsystems were attained by the reliability modes of the systems and the whole system. Finally, a case study was given, which proved that the proposed method could find out the key subsystems rapidly and accurately.

scholarly journals Reliability Estimation under Scarcity of Data: A Comparison of Three Approaches

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Leonardo Leoni ◽  
Alessandra Cantini ◽  
Farshad BahooToroody ◽  
Saeed Khalaj ◽  
Filippo De Carlo ◽  
...  
Keyword(s):  
Likelihood Estimation ◽  
Vital Role ◽  
Reliability Estimation ◽  
Least Square ◽  
Limited Data ◽  
Least Square Estimation ◽  
Process Plants ◽  
Few Data ◽  
Optimal Approach ◽  
Asset Managers

During the last decades, the optimization of the maintenance plan in process plants has lured the attention of many researchers due to its vital role in assuring the safety of operations. Within the process of scheduling maintenance activities, one of the most significant challenges is estimating the reliability of the involved systems, especially in case of data scarcity. Overestimating the average time between two consecutive failures of an individual component could compromise safety, while an underestimate leads to an increase of operational costs. Thus, a reliable tool able to determine the parameters of failure modelling with high accuracy when few data are available would be welcome. For this purpose, this paper aims at comparing the implementation of three practical estimation frameworks in case of sparse data to point out the most efficient approach. Hierarchical Bayesian modelling (HBM), maximum likelihood estimation (MLE), and least square estimation (LSE) are applied on data generated by a simulated stochastic process of a natural gas regulating and metering station (NGRMS), which was adopted as a case of study. The results identify the Bayesian methodology as the most accurate for predicting the failure rate of the considered devices, especially for the equipment characterized by less data available. The outcomes of this research will assist maintenance engineers and asset managers in choosing the optimal approach to conduct reliability analysis either when sufficient data or limited data are observed.

scholarly journals Turning on the Lights: A Meta-Analysis of Residential Electricity Demand Elasticities

2004 ◽  
Vol 36 (1) ◽  
pp. 65-81 ◽  
Author(s):  
James A. Espey ◽  
Molly Espey
Keyword(s):  
Meta Analysis ◽  
Likelihood Estimation ◽  
Electricity Demand ◽  
Least Square ◽  
Least Square Estimation ◽  
Policy Makers ◽  
Income Elasticities ◽  
Price And Income Elasticities ◽  
Residential Electricity ◽  
Residential Demand

Meta-analysis is used to quantitatively summarize previous studies of residential electricity demand to determine if there are factors that systematically affect estimated elasticities. In this study, price and income elasticities of residential demand for electricity from previous studies are used as the dependent variables, with data characteristics, model structure, and estimation technique as independent variables, using both least square estimation of a semilog model and maximum likelihood estimation of a gamma model. The findings of this research can help better inform public policy makers, regulators, and utilities about the responsiveness of residential electricity consumers to price and income changes.

scholarly journals Sine Inverse Lomax Generated Family of Distributions with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Aisha Fayomi ◽  
Ali Algarni ◽  
Abdullah M. Almarashi
Keyword(s):  
Maximum Likelihood ◽  
Real Life ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
New Family ◽  
Estimation Of Model Parameters ◽  
Generated Family ◽  
Family Of Distributions

This paper introduces a new family of distributions by combining the sine produced family and the inverse Lomax generated family. The new proposed family is very interested and flexible more than some old and current families. It has many new models which have many applications in physics, engineering, and medicine. Some fundamental statistical properties of the sine inverse Lomax generated family of distributions as moments, generating function, and quantile function are calculated. Four special models as sine inverse Lomax-exponential, sine inverse Lomax-Rayleigh, sine inverse Lomax-Frèchet and sine inverse Lomax-Lomax models are proposed. Maximum likelihood estimation of model parameters is proposed in this paper. For the purpose of evaluating the performance of maximum likelihood estimates, a simulation study is conducted. Two real life datasets are analyzed by the sine inverse Lomax-Lomax model, and we show that providing flexibility and more fitting than known nine models derived from other generated families.

scholarly journals A Bimodal Extension of the Exponential Distribution with Applications in Risk Theory

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 679
Author(s):  
Jimmy Reyes ◽  
Emilio Gómez-Déniz ◽  
Héctor W. Gómez ◽  
Enrique Calderín-Ojeda
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Rate Function ◽  
Estimation Methods ◽  
Inverse Gaussian ◽  
New Family ◽  
Tail Distribution ◽  
Zero Values ◽  
The Mean ◽  
Positive Support

There are some generalizations of the classical exponential distribution in the statistical literature that have proven to be helpful in numerous scenarios. Some of these distributions are the families of distributions that were proposed by Marshall and Olkin and Gupta. The disadvantage of these models is the impossibility of fitting data of a bimodal nature of incorporating covariates in the model in a simple way. Some empirical datasets with positive support, such as losses in insurance portfolios, show an excess of zero values and bimodality. For these cases, classical distributions, such as exponential, gamma, Weibull, or inverse Gaussian, to name a few, are unable to explain data of this nature. This paper attempts to fill this gap in the literature by introducing a family of distributions that can be unimodal or bimodal and nests the exponential distribution. Some of its more relevant properties, including moments, kurtosis, Fisher’s asymmetric coefficient, and several estimation methods, are illustrated. Different results that are related to finance and insurance, such as hazard rate function, limited expected value, and the integrated tail distribution, among other measures, are derived. Because of the simplicity of the mean of this distribution, a regression model is also derived. Finally, examples that are based on actuarial data are used to compare this new family with the exponential distribution.

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