Weighted Generalization of Rayleigh and Related Class of Distributions

<p>Weighted distributions occur naturally and frequently in research related to reliability, bio-medicine, ecology and in the modeling of clustered sample, heterogeneity, and extraneous variation. In the analysis of intervention data, the expected value of the duration to completion of a random event sampled randomly at the end of its duration turns out to be approximately equal to the expected duration of its random interventions. This is due to the concept of size or length-biased sampling, where the weight function represents the duration of the random event in the life cycle assessment. The case of chronic disease identified by early detection screening programs constitute a length biased (weighted) sampling procedure, as individuals with a long pre-clinical disease phase have a greater probability of being identified. In this research, a new weighted generalization of the Raleigh distribution is constructed. The construction makes use of the "conservability approach" which includes the size or length-biased distribution as a special case. Weighted generalized Raleigh distribution (WGRD) with several weight functions are constructed. The properties of these distributions including behavior of hazard or failure rate and reverse hazard functions, moments, moment generating function, mean, variance, coefficient of variation, coefficient of skewness, coefficient of kurtosis are obtained. Other important properties including entropy (Shannon, beta and generalized) which are measures of the uncertainty in these distributions, and Fisher information which measures the amount of information that a random variable carries about the distribution's unknown parameters are derived and studied. Estimation of the parameters of the weighted generalized Raleigh distribution including the maximum likelihood estimators are derived. Test procedures for weightedness including length-biasedness concerning the Raleigh, generalized Raleigh and weighted generalized Raleigh models are developed.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (restricted to Georgia Southern)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2011

Author dc:creator

• Shi, Xueheng

Contributors dc:contributor

• Charles Champ
• Hani Samawi
• n/a

• ETD
• Weighted distribution
• Weighted Rayleigh distribution
• Reliability function
• Hazard function
• Mathematics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/681

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-1681