scholarly journals Statistical Inference for Geometric Process with the Power Lindley Distribution

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 723 ◽  
Author(s):  
Cenker Bicer
Keyword(s):  
Parameter Estimation ◽  
Mean Squared Error ◽  
Real Data ◽  
Estimation Problem ◽  
Data Sets ◽  
Time Data ◽  
Parameter Estimation Problem ◽  
Data Set ◽  
Monotonic Trend ◽  
Geometric Process

The geometric process (GP) is a simple and direct approach to modeling of the successive inter-arrival time data set with a monotonic trend. In addition, it is a quite important alternative to the non-homogeneous Poisson process. In the present paper, the parameter estimation problem for GP is considered, when the distribution of the first occurrence time is Power Lindley with parameters α and λ . To overcome the parameter estimation problem for GP, the maximum likelihood, modified moments, modified L-moments and modified least-squares estimators are obtained for parameters a, α and λ . The mean, bias and mean squared error (MSE) values associated with these estimators are evaluated for small, moderate and large sample sizes by using Monte Carlo simulations. Furthermore, two illustrative examples using real data sets are presented in the paper.

scholarly journals The Weighted Power Lindley Distribution with Applications on the Life Time Data

2020 ◽  
pp. 225-237
Author(s):  
Aafaq A. Rather ◽  
Gamze Özel
Keyword(s):  
Information Matrix ◽  
Life Time ◽  
Real Data ◽  
Data Sets ◽  
Lifetime Data ◽  
Time Data ◽  
Data Set ◽  
Lindley Distribution ◽  
Power Lindley Distribution ◽  
New Distribution

In this paper, we have proposed a new version of power lindley distribution known as weighted power lindley distribution. The different structural properties of the newly model have been studied. The maximum likelihood estimators of the parameters and the Fishers information matrix have been discussed. It also provides more flexibility to analyze complex real data sets.  An application of the model to a real data set is analyzed using the new distribution, which shows that the weighted power Lindley distribution can be used quite effectively in analyzing real lifetime data.

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.

A RELAX Based Method for Spotlight SAR Imaging

2012 ◽  
Vol 500 ◽  
pp. 362-367
Author(s):  
Xiao Zhen Ren ◽  
Yao Qin ◽  
Hong Liang Fu
Keyword(s):  
Parameter Estimation ◽  
Estimation Problem ◽  
Noisy Environment ◽  
Parameter Estimation Problem ◽  
Imaging Algorithm ◽  
Imaging Results ◽  
Sar Imaging ◽  
Simulation Results ◽  
Noisy Condition

The imaging problem of spotlight SAR is converted to a parameter estimation problem of several monochromatic signals in additive white Gaussian noisy condition in this paper. Moreover, a spotlight SAR imaging algorithm based on RELAX is presented in detail. Traditional polar format algorithm and the presented method are applied to spotlight SAR imaging respectively, and the imaging results are compared. Simulation results show that the polar format algorithm doesn’t give satisfactory imaging results, while the proposed method adapts the noisy environment better and obtains better results.

A Support Based Initialization Algorithm for Categorical Data Clustering

2018 ◽  
Vol 11 (2) ◽  
pp. 53-67
Author(s):  
Ajay Kumar ◽  
Shishir Kumar
Keyword(s):  
Categorical Data ◽  
Selection Process ◽  
Numerical Data ◽  
Real Data ◽  
Data Sets ◽  
Data Set ◽  
Data Object ◽  
Data Points ◽  
Wu Method ◽  
Selection Algorithms

Several initial center selection algorithms are proposed in the literature for numerical data, but the values of the categorical data are unordered so, these methods are not applicable to a categorical data set. This article investigates the initial center selection process for the categorical data and after that present a new support based initial center selection algorithm. The proposed algorithm measures the weight of unique data points of an attribute with the help of support and then integrates these weights along the rows, to get the support of every row. Further, a data object having the largest support is chosen as an initial center followed by finding other centers that are at the greatest distance from the initially selected center. The quality of the proposed algorithm is compared with the random initial center selection method, Cao's method, Wu method and the method introduced by Khan and Ahmad. Experimental analysis on real data sets shows the effectiveness of the proposed algorithm.

scholarly journals Extended Odd Fréchet-G Family of Distributions

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Suleman Nasiru
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Rate Functions ◽  
The Given ◽  
Family Of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.

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