Best Linear Unbiased Estimation of Location and Scale Parameters

N. Balakrishnan and William W. S. Chen
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N. Balakrishnan: McMaster University, Department of Mathematics and Statistics
William W. S. Chen: Internal Revenue Service

Chapter 4 in Handbook of Tables for Order Statistics from Lognormal Distributions with Applications, 1999, pp 13-15 from Springer

Abstract: Abstract Let us now assume that we have a random sample of size n, X 1, X 2,…, X n , from a three-parameter lognormal distribution [obtained by introducing location and scale parameters in (2.3)] with probability density function 4.1 $$ \begin{gathered} f(x|\mu ,\sigma ,k) \hfill \\ \,\,\,\,\,\, = \frac{1}{{\left( {{{(k - 1)}^{{\raise0.7ex\hbox{${ - 1}$} \!\mathord{\left/ {\vphantom {{ - 1} 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}}} + \frac{{x - \mu }}{\sigma }} \right)\sqrt {2\pi \log (k)\sigma } }}{e^{ - {{[\log \{ \sqrt k \left( {1 + {{(k - 1)}^{^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}\frac{{x - \mu }}{\sigma }}}}} \right)\} ]}^2}/(2\log (k)),}} \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\mu - \frac{\sigma }{{\sqrt {k - 1} }}

Keywords: Probability Density Function; Generalize Variance; Order Statistic; Scale Parameter; Column Vector (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-1-4615-5309-0_4

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