Algorithm AS 208: Fitting a Multivariate Logistic Normal Distribution by the Method of Moments

1985 ◽  
Vol 34 (1) ◽  
pp. 81 ◽  
Author(s):  
J. Bacon-Shone
Keyword(s):  
Normal Distribution ◽  
Method Of Moments ◽  
Logistic Normal Distribution

scholarly journals The Discrete Infinite Logistic Normal Distribution

2012 ◽  
Vol 7 (4) ◽  
pp. 997-1034 ◽  
Author(s):  
John Paisley ◽  
Chong Wang ◽  
David M. Blei
Keyword(s):  
Normal Distribution ◽  
Logistic Normal Distribution

scholarly journals Generalised Lambda Distributions by Method of Moments and Maximum Likelihood using the JSE-ASI Returns

2017 ◽  
Vol 9 (1) ◽  
pp. 224
Author(s):  
Peterson Owusu Junior ◽  
Carl H. Korkpoe
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Method Of Moments ◽  
Return Distribution ◽  
Market Returns ◽  
Fit Statistics ◽  
Generalised Method Of Moments ◽  
Tail Events ◽  
Risk Dimensions ◽  
Entire Distribution

The four-parameter generalised lambda distribution provides the flexibility required to describe the key moments of any distribution as compared with the normal distribution which characterises the distribution with only two moments. As markets have increasingly become nervous, the inadequacies of the normal distribution in capturing correctly the tail events and describing fully the entire distribution of market returns have been laid bare. The focus of this paper is to compare the generalised method of moments (GMM) and maximum likelihood essential estimates (MLE) methods as subsets of the GLD for a better fit of JSE All Share Index returns data. We have demonstrated that the appropriate method of the GLD to completely describe the measures of central tendency and dispersion by additionally capturing the risk dimensions of skewness and kurtosis of the return distribution is the Generalised Method of Moments (GMM) with the Kolmogorov-Smirnoff Distance good-of-fit statistics and the quantile-quantile graph. These measures are very important to any investor in the equity markets.

scholarly journals Cell Averaging CFAR Detector with Scale Factor Correction through the Method of Moments for the Log-Normal Distribution

2017 ◽  
Vol 28 (1) ◽  
pp. 27-44 ◽  
Author(s):  
José Raúl Machado Fernández ◽  
Jesús De la Concepción Bacallao Vidal
Keyword(s):  
Normal Distribution ◽  
Method Of Moments ◽  
Scale Factor ◽  
Log Normal ◽  
Log Normal Distribution

Se presenta el nuevo detector LN-MoM-CA-CFAR que tiene una desviación reducida en la tasa de probabilidad de falsa alarma operacional con respecto al valor concebido de diseño. La solución corrige un problema fundamental de los procesadores CFAR que ha sido ignorado en múltiples desarrollos. En efecto, la mayoría de los esquemas previamente propuestos tratan con los cambios bruscos del nivel del clutter mientras que la presente solución corrige los cambios lentos estadísticos de la señal de fondo. Se ha demostrado que estos tienen una influencia marcada en la selección del factor de ajuste multiplicativo CFAR, y consecuentemente en el mantenimiento de la probabilidad de falsa alarma. Los autores aprovecharon la alta precisión que se alcanza en la estimación del parámetro de forma Log-Normal con el MoM, y la amplia aplicación de esta distribución en la modelación del clutter, para crear una arquitectura que ofrece resultados precisos y con bajo costo computacional. Luego de un procesamiento intensivo de 100 millones de muestras Log-Normal, se creó un esquema que, mejorando el desempeño del clásico CA-CFAR a través de la corrección continua de su factor de ajuste, opera con una excelente estabilidad alcanzando una desviación de solamente 0,2884 % para la probabilidad de falsa alarma de 0,01.

The odd log–logistic normal distribution: Theory and applications in analysis of experiments

2016 ◽  
Vol 10 (2) ◽  
pp. 311-335 ◽  
Author(s):  
Altemir da Silva Braga ◽  
Gauss M. Cordeiro ◽  
Edwin M. M. Ortega ◽  
José Nilton da Cruz
Keyword(s):  
Normal Distribution ◽  
Distribution Theory ◽  
Logistic Normal Distribution

scholarly journals A Logistic Normal Mixture Model for Compositional Data Allowing Essential Zeros

2016 ◽  
Vol 45 (4) ◽  
pp. 3-23 ◽  
Author(s):  
John Bear ◽  
Dean Billheimer
Keyword(s):  
Normal Distribution ◽  
Compositional Data ◽  
Normal Mixture ◽  
Dispersion Parameters ◽  
Normal Distributions ◽  
A Value ◽  
Common Location ◽  
Logistic Normal Distribution ◽  
Special Cases ◽  
Support Methods

The usual candidate distributions for modeling compositions, the Dirichlet and the logistic normal distribution, do not include zero components in their support. Methods have been developed and refined for dealing with zeros that are rounded, or due to a value being below a detection level. Methods have also been developed for zeros in compositions arising from count data. However, essential zeros, cases where a component is truly absent, in continuous compositions are still a problem.The most promising approach is based on extending the logistic normal distribution to model essential zeros using a mixture of additive logistic normal distributions of different dimension, related by common parameters. We continue this approach, and by imposing an additional constraint, develop a likelihood, and show ways of estimating parameters for location and dispersion. The proposed likelihood, conditional on parameters for the probability of zeros, is a mixture of additive logistic normal distributions of different dimensions whose location and dispersion parameters are projections of a common location or dispersion parameter. For some simple special cases, we contrast the relative efficiency of different location estimators.

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