Recurrence formula and the maximum likelihood estimation of the age in a simple branching process

1982 ◽  
Vol 19 (4) ◽  
pp. 776-784 ◽  
Author(s):  
M. Adès ◽  
J.-P. Dion ◽  
G. Labelle ◽  
K. Nanthi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimate ◽  
Branching Process ◽  
Negative Binomial ◽  
Recurrence Formula ◽  
Likelihood Estimation ◽  
Likelihood Estimate ◽  
Offspring Distribution ◽  
Watson Process

In this paper, we consider a Bienaymé– Galton–Watson process {Xn; n ≧ 0; Xn = 1} and develop a recurrence formula for P(Xn = k), k = 1, 2, ···. The problem of obtaining the maximum likelihood estimate of the age of the process when p0 = 0 is discussed. Furthermore the maximum likelihood estimate of the age of the process when the offspring distribution is negative binomial (p0 ≠ 0) is obtained, and a comparison with Stigler's estimator (1970) of the age of the process is made.

Recurrence formula and the maximum likelihood estimation of the age in a simple branching process

1982 ◽  
Vol 19 (04) ◽  
pp. 776-784 ◽  
Author(s):  
M. Adès ◽  
J.-P. Dion ◽  
G. Labelle ◽  
K. Nanthi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimate ◽  
Branching Process ◽  
Negative Binomial ◽  
Recurrence Formula ◽  
Likelihood Estimation ◽  
Likelihood Estimate ◽  
Offspring Distribution ◽  
Watson Process

In this paper, we consider a Bienaymé– Galton–Watson process {Xn ; n ≧ 0; Xn = 1} and develop a recurrence formula for P(Xn = k), k = 1, 2, ···. The problem of obtaining the maximum likelihood estimate of the age of the process when p 0 = 0 is discussed. Furthermore the maximum likelihood estimate of the age of the process when the offspring distribution is negative binomial (p 0 ≠ 0) is obtained, and a comparison with Stigler's estimator (1970) of the age of the process is made.

Maximum Likelihood Estimation of Central-City Food Trading Areas

1972 ◽  
Vol 9 (2) ◽  
pp. 154-159 ◽  
Author(s):  
George H. Haines ◽  
Leonard S. Simon ◽  
Marcus Alexis
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimate ◽  
Central City ◽  
Likelihood Estimation ◽  
Likelihood Estimate ◽  
Store Choice ◽  
Home Consumption

A maximum likelihood estimate of the parameter in the Huff model of consumer store choice is derived and its properties are discussed. A method for obtaining a numerical value for the estimator is presented. The procedure is exemplified by estimating trading areas for food purchased for in-home consumption.

A Maximum Likelihood Approach to Density Estimation with Semidefinite Programming

2006 ◽  
Vol 18 (11) ◽  
pp. 2777-2812 ◽  
Author(s):  
Tadayoshi Fushiki ◽  
Shingo Horiuchi ◽  
Takashi Tsuchiya
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Semidefinite Programming ◽  
Density Estimation ◽  
Maximum Likelihood Estimate ◽  
Likelihood Estimation ◽  
Likelihood Estimate ◽  
And Performance ◽  
Low Dimensional ◽  
Two Parameters

Density estimation plays an important and fundamental role in pattern recognition, machine learning, and statistics. In this article, we develop a parametric approach to univariate (or low-dimensional) density estimation based on semidefinite programming (SDP). Our density model is expressed as the product of a nonnegative polynomial and a base density such as normal distribution, exponential distribution, and uniform distribution. When the base density is specified, the maximum likelihood estimation of the polynomial is formulated as a variant of SDP that is solved in polynomial timewith the interior point methods. Since the base density typically contains just one or two parameters, computation of the maximum likelihood estimate reduces to a one- or two-dimensional easy optimization problem with this use of SDP. Thus, the rigorous maximum likelihood estimate can be computed in our approach. Furthermore, such conditions as symmetry and unimodality of the density function can be easily handled within this framework. AIC is used to choose the best model. Through applications to several instances, we demonstrate flexibility of the model and performance of the proposed procedure. Combination with amixture approach is also presented. The proposed approach has possible other applications beyond density estimation. This point is clarified through an application to the maximum likelihood estimation of the intensity function of a nonstationary Poisson process.

scholarly journals Identifying Stabilising Effects on Survey Based Life Satisfaction Using Quasi-maximum Likelihood Estimation

2021 ◽  
Author(s):  
Johannes Klement
Keyword(s):  
Life Satisfaction ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial ◽  
Measurement Instrument ◽  
Likelihood Estimation ◽  
Satisfaction Scale ◽  
Quasi Maximum Likelihood ◽  
The Stability

AbstractTo which extent do happiness correlates contribute to the stability of life satisfaction? Which method is appropriate to provide a conclusive answer to this question? Based on life satisfaction data of the German SOEP, we show that by Negative Binomial quasi-maximum likelihood estimation statements can be made as to how far correlates of happiness contribute to the stabilisation of life satisfaction. The results show that happiness correlates which are generally associated with a positive change in life satisfaction, also stabilise life satisfaction and destabilise dissatisfaction with life. In such as they lower the probability of leaving positive states of life satisfaction and increase the probability of leaving dissatisfied states. This in particular applies to regular exercise, volunteering and living in a marriage. We further conclude that both patterns in response behaviour and the quality of the measurement instrument, the life satisfaction scale, have a significant effect on the variation and stability of reported life satisfaction.

Maximum Likelihood Estimation for the Negative Binomial Dispersion Parameter

Biometrics ◽  
1990 ◽  
Vol 46 (3) ◽  
pp. 863 ◽  
Author(s):  
Walter W. Piegorsch
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Dispersion Parameter

gidm: A command for generalized inflated discrete models

2019 ◽  
Vol 19 (3) ◽  
pp. 698-718
Author(s):  
Yiwei Xia ◽  
Yisu Zhou ◽  
Tianji Cai
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Discrete Distributions ◽  
Discrete Models

In this article, we describe the gidm command for fitting generalized inflated discrete models that deal with multiple inflated values in a distribution. Based on the work of Cai, Xia, and Zhou (Forthcoming, Sociological Methods & Research: Generalized inflated discrete models: A strategy to work with multimodal discrete distributions), generalized inflated discrete models are fit via maximum likelihood estimation. Specifically, the gidm command fits Poisson, negative binomial, multinomial, and ordered outcomes with more than one inflated value. We illustrate this command through examples for count and categorical outcomes.

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).

Some comments concerning a curious singularity

1979 ◽  
Vol 16 (02) ◽  
pp. 440-444 ◽  
Author(s):  
Paul D. Feigin
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Discrete Time ◽  
Maximum Likelihood Estimate ◽  
Likelihood Estimation ◽  
Continuous Observation ◽  
Time Model ◽  
Limit Theory ◽  
Discrete Time Model ◽  
True Value

Consider the maximum likelihood estimation of θ based on continuous observation of the process X, which satisfies dXt = θXtdt + dWt . Feigin (1976) showed that, when suitably normalized, the maximum likelihood estimate is asymptotically normally distributed when the true value of θ ≠ 0. The claim that this asymptotic normality also holds for θ = 0 is shown to be false. The parallel discrete-time model is mentioned and the ramifications of these singularities to martingale central limit theory is discussed.

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