On size-biased Consul distribution

2011 ◽  
Vol 61 (4) ◽  
Author(s):  
Khurshid Mir
Keyword(s):  
Comparative Analysis ◽  
Recurrence Relations ◽  
Estimation Methods ◽  
Central Moments ◽  
Proposed Model ◽  
Generalized Logarithmic Series Distribution ◽  
Logarithmic Series Distribution ◽  
Logarithmic Series

AbstractIn this paper, a size-biased Consul distribution (SBCOND) is defined. Recurrence relations for central moments and the moments about origin are obtained. Different estimation methods for the parameters of the model are discussed. A comparative analysis is done among the three different estimation methods and the proposed model is compared with the generalized logarithmic series distribution (GLSD) and simple Consul distribution.

scholarly journals On Methods of Estimation for Generalized Logarithmic Series Distribution and Its Application to Counts of Red Mites on Apple Leaves

2021 ◽  
Vol 9 (3) ◽  
pp. 151-155
Author(s):  
Fehim J Wani ◽  
Keyword(s):  
Maximum Likelihood ◽  
Estimation Of Parameters ◽  
Chi Square ◽  
Estimation Techniques ◽  
Apple Leaves ◽  
Generalized Logarithmic Series Distribution ◽  
Logarithmic Series Distribution ◽  
Logarithmic Series ◽  
Extra Parameter

The Generalized Logarithmic Series Distribution (GLSD) adds an extra parameter to the usual logarithmic series distribution and was introduced by Jain and Gupta (1973). This distribution has found applications in various fields. The estimation of parameters of generalized logarithmic series distribution was studied by the methods of maximum likelihood, moments, minimum chi square and weighted discrepancies. The GLSD was fitted to counts of red mites on apple leaves and it was observed that all the estimation techniques perform well in estimating the parameters of generalized logarithmic series distribution but with varying degree of non-significance.

scholarly journals Analysis of the multiplicity matching parameter in suffix trees

2005 ◽  
Vol DMTCS Proceedings vol. AD,... (Proceedings) ◽  
Author(s):  
Mark Daniel Ward ◽  
Wojciech Szpankowski
Keyword(s):  
Suffix Tree ◽  
Recurrence Relations ◽  
Complex Analysis ◽  
Analysis Of Algorithms ◽  
Suffix Trees ◽  
Logarithmic Series Distribution ◽  
International Audience ◽  
Number Of Leaves ◽  
Branching Point ◽  
Logarithmic Series

International audience In a suffix tree, the multiplicity matching parameter (MMP) $M_n$ is the number of leaves in the subtree rooted at the branching point of the $(n+1)$st insertion. Equivalently, the MMP is the number of pointers into the database in the Lempel-Ziv '77 data compression algorithm. We prove that the MMP asymptotically follows the logarithmic series distribution plus some fluctuations. In the proof we compare the distribution of the MMP in suffix trees to its distribution in tries built over independent strings. Our results are derived by both probabilistic and analytic techniques of the analysis of algorithms. In particular, we utilize combinatorics on words, bivariate generating functions, pattern matching, recurrence relations, analytical poissonization and depoissonization, the Mellin transform, and complex analysis.

On size-biased generalized logarithmic series distribution

2009 ◽  
Vol 46 (2) ◽  
pp. 157-168
Author(s):  
Anwar Hassan ◽  
Khurshid Mir
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Bayesian Estimation ◽  
Recurrence Relation ◽  
Geometric Series ◽  
Monte Carlo Simulation Technique ◽  
Generalized Logarithmic Series Distribution ◽  
Logarithmic Series Distribution ◽  
Logarithmic Series ◽  
The Relationship

In this paper a size-biased generalized logarithmic series distribution (SBGLSD), a particular case of the weighted generalized logarithmic series distribution, taking the weights as the variate values is defined. The moments and recurrence relation of SBGLSD are obtained. We have also established the relationship between the moments of size-biased generalized logarithmic series distribution and size-biased generalized geometric series distribution (SBGGSD). Bayesian estimation of SBGLSD is discussed and a comparison is made with the generalized logarithmic series distribution (GLSD) by using the Monte Carlo simulation technique.

Sign in / Sign up

Export Citation Format

Share Document