Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

scholarly journals Estimation of density and distribution functions of a Burr X distribution

2018 ◽  
Vol 52 (1) ◽  
pp. 43-59
Author(s):  
AMULYA KUMAR MAHTO ◽  
YOGESH MANI TRIPATH ◽  
SANKU DEY
Keyword(s):  
Mean Squared Error ◽  
Real Data ◽  
Distribution Functions ◽  
Least Square ◽  
Efficient Estimation ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Unbiased Estimation ◽  
Least Square Estimation ◽  
Data Set

Burr type X distribution is one of the members of the Burr family which was originally derived by Burr (1942) and can be used quite effectively in modelling strength data and also general lifetime data. In this article, we consider efficient estimation of the probability density function (PDF) and cumulative distribution function (CDF) of Burr X distribution. Eight different estimation methods namely maximum likelihood estimation, uniformly minimum variance unbiased estimation, least square estimation, weighted least square estimation, percentile estimation, maximum product estimation, Cremer-von-Mises estimation and Anderson-Darling estimation are considered. Analytic expressions for bias and mean squared error are derived. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, a real data set has been analyzed for illustrative purposes.

A COMPARISON OF ESTIMATION METHODS FOR ONE PARAMETER INVERSE GOMPERTZ DISTRIBUTION

2021 ◽  
Vol 21 (3) ◽  
pp. 659-668
Author(s):  
CANER TANIŞ ◽  
KADİR KARAKAYA
Keyword(s):  
Least Squares ◽  
Mean Squared Error ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Real Data ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Gompertz Distribution ◽  
Weighted Least Squares Method ◽  
Von Mises

In this paper, we compare the methods of estimation for one parameter lifetime distribution, which is a special case of inverse Gompertz distribution. We discuss five different estimation methods such as maximum likelihood method, least-squares method, weighted least-squares method, the method of Anderson-Darling, and the method of Crámer–von Mises. It is evaluated the performances of these estimators via Monte Carlo simulations according to the bias and mean-squared error. Furthermore, two real data applications are performed.

scholarly journals New Lindley Half Cauchy Distribution: Theory and Applications

2020 ◽  
Vol 9 (4) ◽  
pp. 1-7
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Cauchy Distribution ◽  
Least Square ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Set ◽  
Von Mises

In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set.

scholarly journals Big-But-Biased Data Analytics for Air Quality

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1551
Author(s):  
Laura Borrajo ◽  
Ricardo Cao
Keyword(s):  
Air Quality ◽  
Data Analytics ◽  
Mean Squared Error ◽  
Smart Cities ◽  
Real Data ◽  
Cumulative Distribution ◽  
Simple Random Sample ◽  
Urban Air ◽  
Data Set ◽  
The Mean

Air pollution is one of the big concerns for smart cities. The problem of applying big data analytics to sampling bias in the context of urban air quality is studied in this paper. A nonparametric estimator that incorporates kernel density estimation is used. When ignoring the biasing weight function, a small-sized simple random sample of the real population is assumed to be additionally observed. The general parameter considered is the mean of a transformation of the random variable of interest. A new bootstrap algorithm is used to approximate the mean squared error of the new estimator. Its minimization leads to an automatic bandwidth selector. The method is applied to a real data set concerning the levels of different pollutants in the urban air of the city of A Coruña (Galicia, NW Spain). Estimations for the mean and the cumulative distribution function of the level of ozone and nitrogen dioxide when the temperature is greater than or equal to 30 ∘C based on 15 years of biased data are obtained.

scholarly journals HALF LOGISTIC MODIFIED EXPONENTIAL DISTRIBUTION: PROPERTIES AND APPLICATIONS

2020 ◽  
pp. 276-287
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Least Square ◽  
Estimation Methods ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Type I ◽  
Data Set ◽  
Von Mises

In this study, we have introduced a three-parameter probabilistic model established from type I half logistic-Generating family called half logistic modified exponential distribution. The mathematical and statistical properties of this distribution are also explored. The behavior of probability density, hazard rate, and quantile functions are investigated. The model parameters are estimated using the three well known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE) and Cramer-Von-Mises estimation (CVME) methods. Further, we have taken a real data set and verified that the presented model is quite useful and more flexible for dealing with a real data set. KEYWORDS— Half-logistic distribution, Estimation, CVME ,LSE, , MLE

scholarly journals A Novel Chen Extension: Theory, Characterizations and Different Estimation Methods

2021 ◽  
Vol 2 ◽  
pp. 1
Author(s):  
Haitham M. Yousof ◽  
Mustafa C. Korkmaz ◽  
G.G. Hamedani ◽  
Mohamed Ibrahim
Keyword(s):  
Numerical Analysis ◽  
Maximum Likelihood ◽  
Weighted Least Squares ◽  
Real Data ◽  
Estimation Methods ◽  
Simulation Studies ◽  
Data Set ◽  
Anderson Darling ◽  
Mean Variance ◽  
Skewness And Kurtosis

In this work, we derive a novel extension of Chen distribution. Some statistical properties of the new model are derived. Numerical analysis for mean, variance, skewness and kurtosis is presented. Some characterizations of the proposed distribution are presented. Different classical estimation methods under uncensored schemes such as the maximum likelihood, Anderson-Darling, weighted least squares and right-tail Anderson–Darling methods are considered. Simulation studies are performed in order to compare and assess the above-mentioned estimation methods. For comparing the applicability of the four classical methods, two application to real data set are analyzed.

scholarly journals A New Three-Parameter Exponential Distribution with Variable Shapes for the Hazard Rate: Estimation and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 135 ◽  
Author(s):  
Ahmed Z. Afify ◽  
Osama Abdo Mohamed
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Sets ◽  
Least Squares Estimators ◽  
Mathematical Properties ◽  
Anderson Darling ◽  
Von Mises

In this paper, we study a new flexible three-parameter exponential distribution called the extended odd Weibull exponential distribution, which can have constant, decreasing, increasing, bathtub, upside-down bathtub and reversed-J shaped hazard rates, and right-skewed, left-skewed, symmetrical, and reversed-J shaped densities. Some mathematical properties of the proposed distribution are derived. The model parameters are estimated via eight frequentist estimation methods called, the maximum likelihood estimators, least squares and weighted least-squares estimators, maximum product of spacing estimators, Cramér-von Mises estimators, percentiles estimators, and Anderson-Darling and right-tail Anderson-Darling estimators. Extensive simulations are conducted to compare the performance of these estimation methods for small and large samples. Four practical data sets from the fields of medicine, engineering, and reliability are analyzed, proving the usefulness and flexibility of the proposed distribution.

scholarly journals ON THE MUTH DISTRIBUTION

2015 ◽  
Vol 20 (3) ◽  
pp. 291-310 ◽  
Author(s):  
Pedro Jodra ◽  
Maria Dolores Jimenez-Gamero ◽  
Maria Virtudes Alba-Fernandez
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Golden Ratio ◽  
Natural Extension ◽  
Real Data ◽  
Random Variable ◽  
Quantile Function ◽  
Lambert W Function ◽  
Data Set ◽  
Monte Carlo Simulation Study

The Muth distribution is a continuous random variable introduced in the context of reliability theory. In this paper, some mathematical properties of the model are derived, including analytical expressions for the moment generating function, moments, mode, quantile function and moments of the order statistics. In this regard, the generalized integro-exponential function, the Lambert W function and the golden ratio arise in a natural way. The parameter estimation of the model is performed by the methods of maximum likelihood, least squares, weighted least squares and moments, which are compared via a Monte Carlo simulation study. A natural extension of the model is considered as well as an application to a real data set.

scholarly journals The Odd Exponentiated Half-Logistic Exponential Distribution: Estimation Methods and Application to Engineering Data

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1684 ◽  
Author(s):  
Maha A. D. Aldahlan ◽  
Ahmed Z. Afify
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Exponential Distribution ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Finite Sample ◽  
Anderson Darling ◽  
Von Mises ◽  
Cramer Von Mises

In this paper, we studied the problem of estimating the odd exponentiated half-logistic exponential (OEHLE) parameters using several frequentist estimation methods. Parameter estimation provides a guideline for choosing the best method of estimation for the model parameters, which would be very important for reliability engineers and applied statisticians. We considered eight estimation methods, called maximum likelihood, maximum product of spacing, least squares, Cramér–von Mises, weighted least squares, percentiles, Anderson–Darling, and right-tail Anderson–Darling for estimating its parameters. The finite sample properties of the parameter estimates are discussed using Monte Carlo simulations. In order to obtain the ordering performance of these estimators, we considered the partial and overall ranks of different estimation methods for all parameter combinations. The results illustrate that all classical estimators perform very well and their performance ordering, based on overall ranks, from best to worst, is the maximum product of spacing, maximum likelihood, Anderson–Darling, percentiles, weighted least squares, least squares, right-tail Anderson–Darling, and Cramér–von-Mises estimators for all the studied cases. Finally, the practical importance of the OEHLE model was illustrated by analysing a real data set, proving that the OEHLE distribution can perform better than some well known existing extensions of the exponential distribution.

scholarly journals The Extended Inverse Weibull Distribution: Properties and Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Said Alkarni ◽  
Ahmed Z. Afify ◽  
I. Elbatal ◽  
M. Elgarhy
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Real Data ◽  
Weibull Model ◽  
Estimation Methods ◽  
Type I ◽  
Data Application ◽  
Inverse Weibull Distribution ◽  
Simulation Results ◽  
Von Mises

This paper proposes the new three-parameter type I half-logistic inverse Weibull (TIHLIW) distribution which generalizes the inverse Weibull model. The density function of the TIHLIW can be expressed as a linear combination of the inverse Weibull densities. Some mathematical quantities of the proposed TIHLIW model are derived. Four estimation methods, namely, the maximum likelihood, least squares, weighted least squares, and Cramér–von Mises methods, are utilized to estimate the TIHLIW parameters. Simulation results are presented to assess the performance of the proposed estimation methods. The importance of the TIHLIW model is studied via a real data application.

Sign in / Sign up

Export Citation Format

Share Document