Estimator and Tests for Coefficient of Variation in Uniform Distribution
نویسندگان
چکیده
Coefficient of variation has been widely used as a measure of precision of measurement equipment in particular for medical laboratories. The objective of this paper is to Inference for the coefficient of variation in uniform distributions. By using the two approaches of central limit theorem and generalized variable, confidence interval for coefficient of variation are considered. The coverage properties of the proposed confidence intervals for proposed two methods are assessment by simulation. An example using data of the approved metrological company from Iran Standard and Industrial Researches Organization is provided. Citation: Hoseini J, Mohammadi A (2012) Estimator and Tests for Coefficient of Variation in Uniform Distribution. J Biomet Biostat 3:149. doi:10.4172/2155-6180.1000149 J Biomet Biostat ISSN:2155-6180 JBMBS, an open access journal Page 2 of 5 Volume 3 • Issue 5 • 1000149 are the MLEs of μ and σ, respectively. Note that ˆ ( )[ ] μ μ μ σ E , = , thus, μ̂ is unbiased estimator of μ. But ˆ μ σ σ σ ( , ) n +1 E [ ] = , n -1 then σ̂ is biased estimator of σ. To generate a unbiased estimator from σ̂ , must use the statistic of σ̂ n+1 . n -1 Also, μ̂ and σ̂ n+1 n -1 are the UMVUEs of μ and σ, respectively. Let μ̂ (1) (n) T = = (X + X ) / 2 and σ̂ (n) (1) R = (2 3 ) = (X X ). Thus, given (μ,σ), (T, R), has a joint probability density ( ) n 2 ( 1) , | , (2 3 ) μ σ σ − − = n n n p t r r ( 3 3 ) (0 2 3 ) 2 2 μ σ μ σ σ − + < < + − < < r r I t I r (2) Note that 2 3( 2) − n T n R is UMVUE of 1/ μ γ σ = [17]. Theorem 1: Let (1) 1 min( ,..., ), = n X X X ( ) 1 max( ,..., ) = n n X X X and 1 / . = =∑n i i X x n Then ( ) (1) 2 3 (0,1) ( ) μ σ − → − d
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