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.

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 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 Bivariate Burr X Generator of Distributions: Properties and Estimation Methods with Applications to Complete and Type-II Censored Samples

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 264 ◽  
Author(s):  
M. El-Morshedy ◽  
Ziyad Ali Alhussain ◽  
Doaa Atta ◽  
Ehab M. Almetwally ◽  
M. S. Eliwa
Keyword(s):  
Real Data ◽  
Bivariate Distribution ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Sets ◽  
Type Ii ◽  
Censored Samples ◽  
Type Ii Censored Data ◽  
Modeling Data

Burr proposed twelve different forms of cumulative distribution functions for modeling data. Among those twelve distribution functions is the Burr X distribution. In statistical literature, a flexible family called the Burr X-G (BX-G) family is introduced. In this paper, we propose a bivariate extension of the BX-G family, in the so-called bivariate Burr X-G (BBX-G) family of distributions based on the Marshall–Olkin shock model. Important statistical properties of the BBX-G family are obtained, and a special sub-model of this bivariate family is presented. The maximum likelihood and Bayesian methods are used for estimating the bivariate family parameters based on complete and Type II censored data. A simulation study was carried out to assess the performance of the family parameters. Finally, two real data sets are analyzed to illustrate the importance and the flexibility of the proposed bivariate distribution, and it is found that the proposed model provides better fit than the competitive bivariate distributions.

scholarly journals A new regression model for bounded response variable: An alternative to the beta and unit-Lindley regression models

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0245627
Author(s):  
Emrah Altun ◽  
M. El-Morshedy ◽  
M. S. Eliwa
Keyword(s):  
Parameter Estimation ◽  
Regression Model ◽  
Regression Models ◽  
Real Data ◽  
Quantile Function ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Response Variable ◽  
Parameter Estimation Methods

A new distribution defined on (0,1) interval is introduced. Its probability density and cumulative distribution functions have simple forms. Thanks to its simple forms, the moments, incomplete moments and quantile function of the proposed distribution are derived and obtained in explicit forms. Four parameter estimation methods are used to estimate the unknown parameter of the distribution. Besides, simulation study is implemented to compare the efficiencies of these parameter estimation methods. More importantly, owing to the proposed distribution, we provide an alternative regression model for the bounded response variable. The proposed regression model is compared with the beta and unit-Lindley regression models based on two real data sets.

scholarly journals THE LOGISTIC INVERSE LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATIONS

2021 ◽  
Vol 09 (01) ◽  
Author(s):  
Ramesh Kumar Joshi ◽  
Keyword(s):  
Goodness Of Fit ◽  
Survival Function ◽  
Continuous Distribution ◽  
Least Square ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Inverse Lomax Distribution

In this article, a three-parameter continuous distribution is introduced called Logistic inverse Lomax distribution. We have discussed some mathematical and statistical properties of the distribution such as the probability density function, cumulative distribution function and hazard rate function, survival function, quantile function, the skewness, and kurtosis measures. The model parameters of the proposed distribution are estimated using three well-known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE), and Cramer-Von-Mises estimation (CVME) methods. The goodness of fit of the proposed distribution is also evaluated by fitting it in comparison with some other existing distributions using a real data set.

scholarly journals The odd log-logistic gompertz lifetime distribution: Properties and applications

2019 ◽  
Vol 56 (1) ◽  
pp. 55-80
Author(s):  
Morad Alizadeh ◽  
Saeid Tahmasebi ◽  
Mohammad Reza Kazemi ◽  
Hamideh Siyamar Arabi Nejad ◽  
G. Hossein G. Hamedani
Keyword(s):  
Survival Data ◽  
Real Data ◽  
Rate Function ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Order Moment ◽  
Failure Rate Function ◽  
Data Set ◽  
Lifetime Distributions ◽  
New Distribution

Abstract In this paper, we introduce a new three-parameter generalized version of the Gompertz model called the odd log-logistic Gompertz (OLLGo) distribution. It includes some well-known lifetime distributions such as Gompertz (Go) and odd log-logistic exponential (OLLE) as special sub-models. This new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a decreasing, increasing and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, the kth order moment, moment generating function and the quantile measure are provided. We discuss maximum likelihood estimation of the OLLGo parameters as well as three other estimation methods from one observed sample. The flexibility and usefulness of the new distribution is illustrated by means of application to a real data set.

scholarly journals Do galactic bars depend on environment?: an information theoretic analysis of Galaxy Zoo 2

2020 ◽  
Vol 501 (1) ◽  
pp. 994-1001
Author(s):  
Suman Sarkar ◽  
Biswajit Pandey ◽  
Snehasish Bhattacharjee
Keyword(s):  
Spatial Distribution ◽  
Mutual Information ◽  
Local Density ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Host Galaxy ◽  
Data Sets ◽  
Data Set ◽  
Information Theoretic

ABSTRACT We use an information theoretic framework to analyse data from the Galaxy Zoo 2 project and study if there are any statistically significant correlations between the presence of bars in spiral galaxies and their environment. We measure the mutual information between the barredness of galaxies and their environments in a volume limited sample (Mr ≤ −21) and compare it with the same in data sets where (i) the bar/unbar classifications are randomized and (ii) the spatial distribution of galaxies are shuffled on different length scales. We assess the statistical significance of the differences in the mutual information using a t-test and find that both randomization of morphological classifications and shuffling of spatial distribution do not alter the mutual information in a statistically significant way. The non-zero mutual information between the barredness and environment arises due to the finite and discrete nature of the data set that can be entirely explained by mock Poisson distributions. We also separately compare the cumulative distribution functions of the barred and unbarred galaxies as a function of their local density. Using a Kolmogorov–Smirnov test, we find that the null hypothesis cannot be rejected even at $75{{\ \rm per\ cent}}$ confidence level. Our analysis indicates that environments do not play a significant role in the formation of a bar, which is largely determined by the internal processes of the host galaxy.

scholarly journals Characteristics and Application of the NHPP Log-Logistic Reliability Model

2018 ◽  
Vol 8 (1) ◽  
pp. 44
Author(s):  
Lutfiah Ismail Al turk
Keyword(s):  
Evaluation Criteria ◽  
Real Data ◽  
Least Square ◽  
Estimation Methods ◽  
Data Sets ◽  
Reliability Model ◽  
Reliability Engineering ◽  
Reliability Models ◽  
Time Domain Data ◽  
Linear Least Square

In this paper, a Nonhomogeneous Poisson Process (NHPP) reliability model based on the two-parameter Log-Logistic (LL) distribution is considered. The essential model’s characteristics are derived and represented graphically. The parameters of the model are estimated by the Maximum Likelihood (ML) and Non-linear Least Square (NLS) estimation methods for the case of time domain data. An application to show the flexibility of the considered model are conducted based on five real data sets and using three evaluation criteria. We hope this model will help as an alternative model to other useful reliability models for describing real data in reliability engineering area.

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