CONSISTENCY OF THE DRIFT PARAMETERS ESTIMATES IN THE FRACTIONAL BROWNIAN DIFFUSION MODEL AND ESTIMATION OF THE HURST PARAMETER BY MAXIMUM LIKELIHOOD METHOD

In this paper, we study the problem of estimating the unknow parameters in a long memory process based on the maximum likelihood method. We consider again a diffusion model involving fractional Brownian motion. Our goal is to study the consistency of the drift parameter estimates depending on the form of the model.

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Slashed Exponentiated Rayleigh Distribution

Revista Colombiana de Estadística ◽

10.15446/rce.v38n2.51673 ◽

2015 ◽

Vol 38 (2) ◽

pp. 453-466 ◽

Cited By ~ 1

Author(s):

Hugo S. Salinas ◽

Yuri A. Iriarte ◽

Heleno Bolfarine

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Real Data ◽

Random Variable ◽

Rayleigh Distribution ◽

Likelihood Method ◽

Independent Random Variables ◽

Parameter Estimates ◽

Positive Data ◽

New Distribution

<p>In this paper we introduce a new distribution for modeling positive data with high kurtosis. This distribution can be seen as an extension of the exponentiated Rayleigh distribution. This extension builds on the quotient of two independent random variables, one exponentiated Rayleigh in the numerator and Beta(q,1) in the denominator with q>0. It is called the slashed exponentiated Rayleigh random variable. There is evidence that the distribution of this new variable can be more flexible in terms of modeling the kurtosis regarding the exponentiated Rayleigh distribution. The properties of this distribution are studied and the parameter estimates are calculated using the maximum likelihood method. An application with real data reveals good performance of this new distribution.</p>

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A Method to Estimate Fibre Length Distribution in Conifers Based on Wood Samples from Increment Cores

Holzforschung ◽

10.1515/hf.2003.038 ◽

2003 ◽

Vol 57 (3) ◽

pp. 248-254 ◽

Cited By ~ 12

Author(s):

T. Mörling ◽

S. Sjöstedt-de Luna ◽

I. Svensson ◽

A. Fries ◽

T. Ericsson

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Length Distribution ◽

Fibre Length ◽

Likelihood Method ◽

Parameter Estimates ◽

Normal Distributions ◽

Breast Height ◽

Pine Trees ◽

Truncated Normal

Summary We propose a method to estimate fibre length distribution in conifers based on wood samples from increment cores processed by automatic optical fibre-analysers. Automatic fibre-analysers are unable to distinguish: a) fibres from other tissues, “fines”, and b) cut from uncut fibres. However, our proposed method can handle these problems if the type of distributions that fibre lengths and fines follow is known. In our study the length distributions of fines and fibres were assumed to follow truncated normal distributions, characterised by means and standard deviations of the two distributions. Parameter estimates were obtained by the maximum likelihood method. Wood samples from two 22-year-old Scots pine trees at breast height were used to evaluate the performance of the method. From stem discs at 1.5 m, adjacent samples of 5 mm increment cores and wood pieces were taken. The cores were trimmed 1 mm at each side and samples were, after maceration, analysed in a Kajaani FiberLab 3.0. The results showed that the method works well and gives a possibility to distinguish fine and fibre length distribution.

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