Negative binomial improved second degree lindley distribution and its application

2020 ◽  
pp. 569-581
Author(s):  
R. Ashly ◽  
C. S. Rajitha
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Data Set ◽  
Factorial Moments ◽  
Lindley Distribution ◽  
Second Degree

The objective of this paper is to introduce a new two parameter mixed negative binomial distribution, namely negative binomial-improved second degree Lindley(NB-ISL) distribution. This distribution is obtained by mixing the negative binomial distribution with the improved second degree Lindley distribution. Many mixed distributions have been used in the literature for modeling the over dispersed count data, which provide a better fit compared to the Poisson and negative binomial distribution. In addition, we present the basic statistical properties of the new distribution such as factorial moments, mean and variance and the behavior of mean, variance and coefficient of variation are also discussed. Parameter estimation is implemented by using maximum likelihood estimation method. The performance of the NB-ISL distribution is shown in practice by applying it on real data set and compare it with some well-known count distributions. The result shows that the negative binomial-improved second degree Lindley distribution provides a better fit compared to Poisson, negative binomial and negative binomial-Lindley distributions.

scholarly journals Suitability of Several Statistical Models to Simulate Observed Distribution of Sample Test Results in Inspections of Aflatoxin-Contaminated Peanut Lots

1996 ◽  
Vol 79 (4) ◽  
pp. 981-988 ◽  
Author(s):  
Thomas Whitaker ◽  
Francis Giesbrecht ◽  
Jeremy Wu
Keyword(s):  
Parameter Estimation ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Statistical Models ◽  
Negative Binomial ◽  
Estimation Method ◽  
Likelihood Method ◽  
Model Parameters ◽  
Test Results ◽  
Parameter Estimation Method

Abstract The acceptability of 10 theoretical distributions to simulate observed distribution of sample aflatoxin test results was evaluated by using 2 parameter estimation methods and 3 goodness of fit (GOF) tests. All theoretical distributions were compared with 120 observed distributions of aflatoxin test results of farmers' stock peanuts. For a given parameter estimation method and GOF test, the negative binomial distribution had the highest percentage of statistically acceptable fits. The log normal and Poisson-gamma (gamma shape parameter = 0.5) distributions had slightly fewer but an almost equal percentage of acceptable fits. For the 3 most acceptable statistical models, the negative binomial had the greatest percentage of best or closest fits. Both the parameter estimation method and the GOF test had an influence on which theoretical distribution had the largest number of acceptable fits. All theoretical distributions, except the negative binomial distribution, had more acceptable fits when model parameters were determined by the maximum likelihood method. The negative binomial had slightly more acceptable fits when model parameters were estimated by the method of moments. The results also demonstrated the importance of using the same GOF test for comparing the acceptability of several theoretical distributions.

scholarly journals On Properties of the Bimodal Skew-Normal Distribution and an Application

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 703
Author(s):  
David Elal-Olivero ◽  
Juan F. Olivares-Pacheco ◽  
Osvaldo Venegas ◽  
Heleno Bolfarine ◽  
Héctor W. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Skew Normal Distribution ◽  
Data Set ◽  
Normal Distributions ◽  
Stochastic Representations ◽  
Skew Normal

The main object of this paper is to develop an alternative construction for the bimodal skew-normal distribution. The construction is based upon a study of the mixture of skew-normal distributions. We study some basic properties of this family, its stochastic representations and expressions for its moments. Parameters are estimated using the maximum likelihood estimation method. A simulation study is carried out to observe the performance of the maximum likelihood estimators. Finally, we compare the efficiency of the new distribution with other distributions in the literature using a real data set. The study shows that the proposed approach presents satisfactory results.

scholarly journals On Poisson-Weighted Lindley Distribution and Its Applications

2019 ◽  
Vol 11 (1) ◽  
pp. 1-13
Author(s):  
R. Shanker ◽  
K. K. Shukla
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial Distribution ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Poisson Mixture ◽  
Lindley Distribution ◽  
Generalized Poisson ◽  
And Behavior

In this paper the nature and behavior of its coefficient of variation, skewness, kurtosis and index of dispersion of Poisson- weighted Lindley distribution (P-WLD), a Poisson mixture of weighted Lindley distribution, have been proposed and the nature and behavior have been explained graphically. Maximum likelihood estimation has been discussed to estimate its parameters. Applications of the proposed distribution have been discussed and its goodness of fit has been compared with Poisson distribution (PD), Poisson-Lindley distribution (PLD), negative binomial distribution (NBD) and generalized Poisson-Lindley distribution (GPLD).

The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data

2020 ◽  
Vol 70 (4) ◽  
pp. 917-934
Author(s):  
Muhammad Mansoor ◽  
Muhammad Hussain Tahir ◽  
Gauss M. Cordeiro ◽  
Sajid Ali ◽  
Ayman Alzaatreh
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Hazard Rate ◽  
Negative Binomial ◽  
Real Data ◽  
Moment Generating Function ◽  
Estimation Methods ◽  
Model Parameters ◽  
Proposed Model ◽  
Rate Functions

AbstractA generalization of the Lindley distribution namely, Lindley negative-binomial distribution, is introduced. The Lindley and the exponentiated Lindley distributions are considered as sub-models of the proposed distribution. The proposed model has flexible density and hazard rate functions. The density function can be decreasing, right-skewed, left-skewed and approximately symmetric. The hazard rate function possesses various shapes including increasing, decreasing and bathtub. Furthermore, the survival and hazard rate functions have closed form representations which make this model tractable for censored data analysis. Some general properties of the proposed model are studied such as ordinary and incomplete moments, moment generating function, mean deviations, Lorenz and Bonferroni curve. The maximum likelihood and the Bayesian estimation methods are utilized to estimate the model parameters. In addition, a small simulation study is conducted in order to evaluate the performance of the estimation methods. Two real data sets are used to illustrate the applicability of the proposed model.

Signatures Extraction of Ship Radiated Noise Based on Passive Sonar

2014 ◽  
Vol 568-570 ◽  
pp. 233-237 ◽  
Author(s):  
Hong Ji Wang ◽  
Ri Jie Yang ◽  
Jian Hui Han
Keyword(s):  
Feature Extraction ◽  
Shallow Water ◽  
Kalman Filtering ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Underwater Noise ◽  
Data Set ◽  
Radiated Noise ◽  
Extraction Algorithm

By combining likelihood estimation method and Kalman filtering tracking approach, feature extraction algorithm was developed in this paper to extract the harmonic feature from the underwater noise radiated by different kinds of ships. The ability of harmonic features extrication algorithm is demonstrated by simulation and real shallow water data set comprised of a number of ships. The processing results of real data set also show that he harmonics of different kinds of ships can be used to separate from each other.

NEW ANALYSIS OF MULTIPLICITY DISTRIBUTIONS

1993 ◽  
Vol 08 (29) ◽  
pp. 2747-2752 ◽  
Author(s):  
I. M. DREMIN
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
High Multiplicity ◽  
Factorial Moments ◽  
Large Rank ◽  
Multiplicity Distributions

The ratio of cumulant to factorial moments is proposed as a new measure of multiplicity distributions. Its advantages and shortcomings are discussed using the negative binomial distribution and several QCD-inspired functions as examples. Its asymptotic at large rank reveals tiny features of high multiplicity tails of distributions which can become especially important at LHC and SSC.

Marginal likelihood estimation of negative binomial parameters with applications to RNA-seq data

Biostatistics ◽  
2017 ◽  
Vol 18 (4) ◽  
pp. 637-650 ◽  
Author(s):  
Luis León-Novelo ◽  
Claudio Fuentes ◽  
Sarah Emerson
Keyword(s):  
Negative Binomial ◽  
Marginal Likelihood ◽  
Hypothesis Test ◽  
Likelihood Estimation ◽  
Real Data ◽  
Rna Seq ◽  
Data Set ◽  
Bayesian Hierarchical ◽  
Proposed Model ◽  
Bayesian Hypothesis Test

SUMMARY RNA-Seq data characteristically exhibits large variances, which need to be appropriately accounted for in any proposed model. We first explore the effects of this variability on the maximum likelihood estimator (MLE) of the dispersion parameter of the negative binomial distribution, and propose instead to use an estimator obtained via maximization of the marginal likelihood in a conjugate Bayesian framework. We show, via simulation studies, that the marginal MLE can better control this variation and produce a more stable and reliable estimator. We then formulate a conjugate Bayesian hierarchical model, and use this new estimator to propose a Bayesian hypothesis test to detect differentially expressed genes in RNA-Seq data. We use numerical studies to show that our much simpler approach is competitive with other negative binomial based procedures, and we use a real data set to illustrate the implementation and flexibility of the procedure.

scholarly journals Classification of RNA-Seq Data via Gaussian Copulas

2017 ◽  
Author(s):  
Qingyang Zhang
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Natural Extension ◽  
Real Data ◽  
Discrete Distributions ◽  
Gaussian Copula ◽  
Rna Seq ◽  
Independence Assumption ◽  
Discriminant Score

AbstractRNA-sequencing (RNA-Seq) has become a preferred option to quantify gene expression, because it is more accurate and reliable than microarrays. In RNA-Seq experiments, the expression level of a gene is measured by the count of short reads that are mapped to the gene region. Although some normal-based statistical methods may also be applied to log-transformed read counts, they are not ideal for directly modeling RNA-Seq data. Two discrete distributions, Poisson distribution and negative binomial distribution, have been commonly used in the literature to model RNA-Seq data, where the latter is a natural extension of the former with allowance of overdispersion. Due to the technical difficulty in modeling correlated counts, most existing classifiers based on discrete distributions assume that genes are independent of each other. However, as we show in this paper, the independence assumption may cause non-ignorable bias in estimating the discriminant score, making the classification inaccurate. To this end, we drop the independence assumption and explicitly model the dependence between genes using Gaussian copula. We apply a Bayesian approach to estimate covariance matrix and the overdispersion parameter in negative binomial distribution. Both synthetic data and real data are used to demonstrate the advantages of our model.

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