scholarly journals Uma proposta para identificação de outliers multivariados

2018 ◽  
Vol 40 ◽  
pp. 40
Author(s):  
Josino José Barbosa ◽  
Tiago Martins Pereira ◽  
Fernando Luiz Pereira de Oliveira
Keyword(s):  
Probability Distributions ◽  
Estimation Method ◽  
Real Data ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Inverse Power ◽  
Test Statistic ◽  
Lindley Distribution ◽  
Power Lindley Distribution ◽  
Inverse Lindley Distribution

In the last years several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible relative to the behaviors of the density and hazard rate functions. For instance, Ghitany et al. (2013) proposed a new generalization of the Lindley distribution, called power Lindley distribution, whereas Sharma et al. (2015a) proposed the inverse Lindley distribution. From these two generalizations Barco et al. (2017) studied the inverse power Lindley distribution, also called by Sharma et al. (2015b) as generalized inverse Lindley distribution. Considering the inverse power Lindley distribution, in this paper is evaluate the performance, through Monte Carlo simulations, with respect to the bias and consistency of nine different methods of estimations (the maximum likelihood method and eight others based on the distance between the empirical and theoretical cumulative distribution function). The numerical results showed a better performance of the estimation method based on the Anderson-Darling test statistic. This conclusion is also observed in the analysis of two real data sets.

scholarly journals Estimation of Stress Strength Reliability in Single Component Models for Different Distributions

2019 ◽  
pp. 1-10
Author(s):  
Nafeesa Bashir ◽  
Raeesa Bashir ◽  
T. R. Jan ◽  
Shakeel A. Mir
Keyword(s):  
Likelihood Estimation ◽  
Inverse Power ◽  
Reliability Parameter ◽  
Strength Parameters ◽  
Lindley Distribution ◽  
Power Lindley Distribution ◽  
Method Of Maximum Likelihood ◽  
R Programming ◽  
Component Models ◽  
Inverse Lindley Distribution

This paper aims to estimate the stress-strength reliability parameter R = P(Y < X), considering the two different cases of stress strength parameters, when the strength ‘X’ follows exponentiated inverse power Lindley distribution ,extended inverse Lindley and Stress ‘Y’ follows inverse power Lindley distribution and inverse Lindley distribution. The method of maximum likelihood estimation is used to obtain the reliability estimators. Illustrations are provided using R programming.

Marshall-Olkin Extended Power Lindley Distribution with Application

2018 ◽  
Vol 2 (2) ◽  
pp. 84
Author(s):  
Rafif Hibatullah ◽  
Yekti Widyaningsih ◽  
Sarini Abdullah
Keyword(s):  
Density Function ◽  
Model Comparison ◽  
Scale Parameter ◽  
Survival Function ◽  
Weibull Model ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Lindley Distribution ◽  
Power Lindley Distribution ◽  
Extended Power

Lindley distribution was introduced by Lindley (1958) in the context of Bayes inference. Its density function is obtained by mixing the exponential distribution, with scale parameter β, and the gamma distribution, with shape parameter 2 and scale parameter β. Recently, a new generalization of the Lindley distribution was proposed by Ghitany et al. (2013), called power Lindley distribution. This paper will introduce an extension of the power Lindley distribution using the Marshall-Olkin method, resulting in Marshall-Olkin Extended Power Lindley (MOEPL) distribution. The MOEPL distribution offers a flexibility in representing data with various shapes. This flexibility is due to the addition of a parameter to the power Lindley distribution. Some properties of the MOEPL were explored, such as probability density function (pdf), cumulative distribution function (cdf), hazard rate, survival function, quantiles, and moments. Estimation of the MOEPL parameters was conducted using maximum likelihood method. The proposed distribution was applied to data. The results were given which illustrate the MOEPL distribution and were compared to Lindley, power Lindley, gamma, and Weibull. Model comparison using the log likelihood, AIC, and BIC showed that MOEPL fit the data better than the other distributions.

scholarly journals A New Parametric Life Family of Distributions: Properties, Copula and Modeling Failure and Service Times

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1462
Author(s):  
Mansour Shrahili ◽  
Naif Alotaibi
Keyword(s):  
Maximum Likelihood ◽  
Probability Distributions ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
New Family ◽  
Renyi’S Entropy

A new family of probability distributions is defined and applied for modeling symmetric real-life datasets. Some new bivariate type G families using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula and Renyi’s entropy copula are derived. Moreover, some of its statistical properties are presented and studied. Next, the maximum likelihood estimation method is used. A graphical assessment based on biases and mean squared errors is introduced. Based on this assessment, the maximum likelihood method performs well and can be used for estimating the model parameters. Finally, two symmetric real-life applications to illustrate the importance and flexibility of the new family are proposed. The symmetricity of the real data is proved nonparametrically using the kernel density estimation method.

scholarly journals A Probability Density Function Generator Based on Deep Learning

2018 ◽  
Author(s):  
Chi-Hua Chen ◽  
Fangying Song ◽  
Feng-Jang Hwang ◽  
Ling Wu
Keyword(s):  
Deep Learning ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Probability Distributions ◽  
Real Data ◽  
Learning Model ◽  
Cumulative Distribution ◽  
Function Generator ◽  
Deep Learning Model

To generate a probability density function (PDF) for fitting probability distributions of real data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be adopted as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of trained deep learning model can be used to estimate the PDF. To evaluate the proposed method, numerical experiments with single and mixed distributions are performed. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method.

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 Moment based Estimation for the Shape Parameters, Effect it on Some Probability Statistical Distributions Using the Moment Method and Maximum Likelihood Method

2020 ◽  
Vol 5 (6) ◽  
pp. 979-986
Author(s):  
Hassan Tawakol A. Fadol
Keyword(s):  
Maximum Likelihood ◽  
Shape Parameter ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Estimation Method ◽  
Simulation Method ◽  
Likelihood Method ◽  
Inductive Method ◽  
Binomial Distributions ◽  
Best Estimate

The purpose of this paper was to identify the values of the parameters of the shape of the binomial, bias one and natural distributions. Using the estimation method and maximum likelihood Method, the criterion of differentiation was used to estimate the shape parameter between the probability distributions and to arrive at the best estimate of the parameter of the shape when the sample sizes are small, medium, The problem was to find the best estimate of the characteristics of the society to be estimated so that they are close to the estimated average of the mean error squares and also the effect of the estimation method on estimating the shape parameter of the distributions at the sizes of different samples In the values of the different shape parameter, the descriptive and inductive method was selected in the analysis of the data by generating 1000 random numbers of different sizes using the simulation method through the MATLAB program. A number of results were reached, 10) to estimate the small shape parameter (0.3) for binomial distributions and Poisson and natural and they can use the Poisson distribution because it is the best among the distributions, and to estimate the parameter of figure (0.5), (0.7), (0.9) Because it is better for binomial binomial distributions, when the size of a sample (70) for a teacher estimate The small figure (0.3) of the binomial and boson distributions and natural distributions can be used for normal distribution because it is the best among the distributions.

Zero-truncated Poisson-Lindley distribution

2021 ◽  
pp. 40-50
Author(s):  
Afida Nurul Hilma ◽  
Dian Lestari ◽  
Sindy Devila
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Lindley Distribution ◽  
Count Distribution ◽  
Distribution Parameters ◽  
Counting Distribution ◽  
Over Dispersion

In order to find a counting distribution that can handle the condition when the data has no zero-count. Distribution named Zero-truncated Poisson-Lindley distribution is developed. It can handle the condition when the data has no zero-count both in over-dispersion and under-dispersion. In this paper, characteristics of Zero-truncated Poisson-Lindley distribution are obtained and estimate distribution parameters using the maximum likelihood method. Then, the application of the model to real data is given.

scholarly journals A New Discrete Analog of the Continuous Lindley Distribution, with Reliability Applications

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 603
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Abdul Hadi N. Ahmed ◽  
Ahmed Z. Afify
Keyword(s):  
Goodness Of Fit ◽  
Negative Binomial ◽  
Real Data ◽  
Moment Generating Function ◽  
Discrete Analog ◽  
Bias Reduction ◽  
Discrete Distributions ◽  
Likelihood Method ◽  
Probability Mass Function ◽  
Lindley Distribution

In this paper, we propose and study a new probability mass function by creating a natural discrete analog to the continuous Lindley distribution as a mixture of geometric and negative binomial distributions. The new distribution has many interesting properties that make it superior to many other discrete distributions, particularly in analyzing over-dispersed count data. Several statistical properties of the introduced distribution have been established including moments and moment generating function, residual moments, characterization, entropy, estimation of the parameter by the maximum likelihood method. A bias reduction method is applied to the derived estimator; its existence and uniqueness are discussed. Applications of the goodness of fit of the proposed distribution have been examined and compared with other discrete distributions using three real data sets from biological sciences.

scholarly journals A Generalised Exponential-Lindley Mixture of Poisson Distribution

2019 ◽  
Vol 3 ◽  
pp. 11-20
Author(s):  
Binod Kumar Sah ◽  
A. Mishra
Keyword(s):  
Poisson Distribution ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Mixture Distribution ◽  
Discrete Data ◽  
Likelihood Method ◽  
P Value ◽  
Data Set ◽  
Lindley Distribution ◽  
First Four Moments

Background: The exponential and the Lindley (1958) distributions occupy central places among the class of continuous probability distributions and play important roles in statistical theory. A Generalised Exponential-Lindley Distribution (GELD) was given by Mishra and Sah (2015) of which, both the exponential and the Lindley distributions are the particular cases. Mixtures of distributions form an important class of distributions in the domain of probability distributions. A mixture distribution arises when some or all the parameters in a probability function vary according to certain probability law. In this paper, a Generalised Exponential- Lindley Mixture of Poisson Distribution (GELMPD) has been obtained by mixing Poisson distribution with the GELD. Materials and Methods: It is based on the concept of the generalisations of some continuous mixtures of Poisson distribution. Results: The Probability mass of function of generalized exponential-Lindley mixture of Poisson distribution has been obtained by mixing Poisson distribution with GELD. The first four moments about origin of this distribution have been obtained. The estimation of its parameters has been discussed using method of moments and also as maximum likelihood method. This distribution has been fitted to a number of discrete data-sets which are negative binomial in nature and it has been observed that the distribution gives a better fit than the Poisson–Lindley Distribution (PLD) of Sankaran (1970). Conclusion: P-value of the GELMPD is found greater than that in case of PLD. Hence, it is expected to be a better alternative to the PLD of Sankaran for similar type of discrete data-set which is negative binomial in nature.

scholarly journals Alpha Power Transformed Lindley Distribution

2021 ◽  
pp. 130-142
Author(s):  
L A Rosa ◽  
S Nurrohmah ◽  
I Fithriani
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Hazard Rate ◽  
Survival Function ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Alpha Power ◽  
Lindley Distribution ◽  
Modelling Data

The one parameter Lindley distribustion (theta) has been widely used in various field such as biology, technique, medical, and industries. Lindley distribution is capable for modelling data with monotone increasing hazard rate. However, in real life, there are situations where the hazard rate is not monotone. Therefore, to enhance the Lindley distribution capabilitiesfor modelling data, a modification can be used by using Alpha Power Transformed method. The result of the modification of Lindley distribution is commonly called Alpha Power Transformed Lindley distribution (APTL) distribution that has two parameters (alpha, theta). This new APTL distribution is appropriate in modelling data with decreasing or unimodal shaped of probability density function, and has hazard rates with increasing, decreasing, and upside-down bathtub shaped. The properties of the proposed distribution are discussed include probability density function, cumulative distribution function, survival function, hazard rate function, moment generating function, and rth moment. Themodel parameters are obtained using maximum likelihood method. The waiting time data is used as an illustration to describe the utility of APTL distribution.

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