scholarly journals A Distribuição Half-Normal Generalizada Discreta: uma distribuição alternativa na análise de dados de contagem

2019 ◽  
Vol 41 ◽  
pp. 27
Author(s):  
Josmar Mazucheli ◽  
Ricardo Puziol De Oliveira ◽  
Jean Carlos Cardoso
Keyword(s):  
Maximum Likelihood Method ◽  
Negative Binomial ◽  
Survival Function ◽  
Discrete Distributions ◽  
Likelihood Method ◽  
Discrete Version ◽  
Data Sets ◽  
Continuous Version ◽  
Binomial Distributions ◽  
General Data

In general, data that are obtained by counting processes, strictly discrete or discretized (from truncations and/or rounding), are analyzed, without exhaustion, by the Geometric, Logarithmic, Poisson and Negative Binomial distributions. In recent years a large number of discrete distributions have been proposed in the literature from the discretization of continuous random variables. Many of the discretization methods preserve one or more characteristics of the continuous version, with the proposal of Nakagawa e Osaki (1975) being the most used. In this paper, from this methodology, which makes use of the survival function, we propose the discrete version of the continuous generalized Half-Normal distribution, introduced in the literature by Cooray e Ananda (2008). Some of its properties are discussed and Monte Carlo simulations evaluate the bias and accuracy of the estimates obtained by the maximum likelihood method and method of moments. Some discrete data sets found in the literature are considered to illustrate the applicability of the proposed distribution.

scholarly journals Weighted Negative Binomial Poisson-Lindley Distribution with Actuarial Applications

2018 ◽  
Author(s):  
Hossein Zamani ◽  
Noriszura Ismail ◽  
Marzieh Shekari
Keyword(s):  
Maximum Likelihood Method ◽  
Negative Binomial ◽  
Statistical Tests ◽  
Discrete Distribution ◽  
Likelihood Method ◽  
Weighted Version ◽  
Lindley Distribution ◽  
Weighted Distribution ◽  
Binomial Distributions ◽  
Over Dispersion

This study introduces a new discrete distribution which is a weighted version of Poisson-Lindley distribution. The weighted distribution is obtained using the negative binomial weight function and can be fitted to count data with over-dispersion. The p.m.f., p.g.f. and simulation procedure of the new weighted distribution, namely weighted negative binomial Poisson-Lindley (WNBPL), are provided. The maximum likelihood method for parameter estimation is also presented. The WNBPL distribution is fitted to several insurance datasets, and is compared to the Poisson and negative binomial distributions in terms of several statistical tests.

scholarly journals A Two Parameter Discrete Lindley Distribution

2016 ◽  
Vol 39 (1) ◽  
pp. 45-61 ◽  
Author(s):  
Tassaddaq Hussain ◽  
Muhammad Aslam ◽  
Munir Ahmad
Keyword(s):  
Negative Binomial ◽  
Parameters Estimation ◽  
Discrete Distributions ◽  
Likelihood Method ◽  
Data Sets ◽  
Factorial Moments ◽  
Lindley Distribution ◽  
Generalized Poisson ◽  
Gamma Distributions ◽  
Two Parameter

<p>In this article we have proposed and discussed a two parameter discrete Lindley distribution. The derivation of this new model is based on a two step methodology i.e. mixing then discretizing, and can be viewed as a new generalization of geometric distribution. The proposed model has proved itself as the least loss of information model when applied to a number of data sets (in an over and under dispersed structure). The competing models such as Poisson, Negative binomial, Generalized Poisson and discrete gamma distributions are the well known standard discrete distributions. Its Lifetime classification, kurtosis, skewness, ascending and descending factorial moments as well as its recurrence relations, negative moments, parameters estimation via maximum likelihood method, characterization and discretized bi-variate case are presented.</p>

scholarly journals The extended odd family of probability distributions with practice to a submodel

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3855-3867 ◽  
Author(s):  
Hassan Bakouch ◽  
Christophe Chesneau ◽  
Muhammad Khan
Keyword(s):  
Heavy Tails ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Tuning Parameter ◽  
Data Sets ◽  
New Family ◽  
Rate Functions ◽  
Special Case ◽  
Family Of Distributions

In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then, we study a special case dealing with the standard loglogistic distribution and the modifiedWeibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions with applications to two practical data sets.

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.

scholarly journals On Modified Burr XII-Inverse Weibull Distribution: Development, Properties, Characterizations and Applications

2020 ◽  
pp. 721-735
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Haitham M. Yousof ◽  
Azeem Ali ◽  
Munir Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Quarterly Earnings ◽  
Inverse Weibull Distribution

A flexible lifetime distribution with increasing, decreasing, inverted bathtub and modified bathtub hazard rate called Modified Burr XII-Inverse Weibull (MBXII-IW) is introduced and studied. The density function of MBXII-IW is exponential, left-skewed, right-skewed and symmetrical shaped.  Descriptive measures on the basis of quantiles, moments, order statistics and reliability measures are theoretically established. The MBXII-IW distribution is characterized via different techniques. Parameters of MBXII-IW distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of MBXII-IW distribution is demonstrated by its application to real data sets: serum-reversal times and quarterly earnings.

Application of the maximum‐likelihood method (MLM) for sonic velocity logging

Geophysics ◽  
1986 ◽  
Vol 51 (3) ◽  
pp. 780-787 ◽  
Author(s):  
Kai Hsu ◽  
Arthur B. Baggeroer
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Laboratory Data ◽  
Signal Strength ◽  
Likelihood Method ◽  
Data Sets ◽  
Normalization Procedure ◽  
Computational Requirement ◽  
Full Waveforms ◽  
Schlumberger Array

Modern digital sonic tools can record full waveforms using an array of receivers. The recorded waveforms are extremely complicated because wave components overlap in time. Conventional beamforming approaches, such as semblance processing, while robust, sometimes do not resolve the interfering wave components propagating at similar speeds, such as multiple compressional arrivals due to the formation alteration surrounding the borehole. Here the maximum‐likelihood method (MLM), a high‐resolution array processing algorithm, is modified and applied to process borehole array sonic data. Extensive modifications of the original MLM algorithm were necessary because of the transient character of the sonic data and its effect upon the spectral covariance matrix. We applied MLM to several array sonic data sets, including laboratory data, synthetic waveforms, and field data taken by a Schlumberger array sonic tool. MLM’s slowness resolution is demonstrated in resolving a secondary compressional arrival from the primary compressional arrival in an altered formation, and the formation compressional arrival in the presence of a stronger casing arrival in an unbonded cased hole. In comparison with the semblance processing results, the MLM results clearly show a better slowness resolution. However, in the case of a weak formation arrival, the semblance processing tends to enhance and resolve the weak arrival by the semblance normalization procedure, while the MLM, designed to estimate the signal strength, does not. The heavy computational requirement (mainly, many matrix inversions) in the MLM makes it much slower than semblance processing, which may prohibit implementation of the MLM algorithm in a real‐time environment.

The influence of water temperature and pH on the survival of Fasciola hepatica miracidia

Parasitology ◽  
1984 ◽  
Vol 88 (1) ◽  
pp. 97-104 ◽  
Author(s):  
G. Smith ◽  
B. T. Grenfell
Keyword(s):  
Maximum Likelihood Method ◽  
Fasciola Hepatica ◽  
Good Description ◽  
Survival Function ◽  
Experimental Studies ◽  
Likelihood Method ◽  
Confidence Limits ◽  
Mean Values ◽  
Influence Of Water ◽  
The Mean

SUMMARYExperimental studies on the survival of Fasciola hepatica miracidia show no evidence that miracidial mortality varies with the pH of the medium, at least in the range 6·0–8·0. On the other hand, miracidial mortality is shown to vary with both the temperature of the medium and the age of the larvae. The mean expected life-span of the miracidium decreases from about 35 h at 6°C to about 6° h at 25° C. The Gompertz survival function provides a good description of the miracidial survivorship curves over the range of temperatures used, and we describe, a maximum likelihood method of estimating the mean values of the parameters of this function, together with their approximate 95% confidence limits.

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.

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 New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 440 ◽  
Author(s):  
Abdulhakim A. Al-babtain ◽  
I. Elbatal ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Clayton Copula ◽  
Mathematical Properties

In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets.

Sign in / Sign up

Export Citation Format

Share Document