Efficiency of Modified Exponential Dual to Ratio-Product-Cum Type Estimator under Stratified Sampling Using Two Auxiliary Variables
Haruna Suleiman *
Department of Statistics, Niger State Polytechnic, Zungeru, Nigeria.
Jibrin Abdullahi Yafu
Department of Statistics, Federal Polytechnic, Bida, Niger State, Nigeria.
Audu Ahmed
Department of Statistics, Usmanu Danfodiyo University, Sokoto, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Separate and Combined dual to ratio-product-cum estimators of the population mean under stratified random sampling scheme are suggested using the ideas and the analogy of (Walsh [1], Reddy [2], Tripathi [3]) and adopted strategy initiated by (Koyuncu and Kadilar [4], Singh et al., [5], Yasmeen et al., [6], Rather and Kadilar [7]) as well as the two auxiliaries variable. Asymptotic properties of proposed estimators such as BIASs, MSEs and MMSEs up to first order of approximation by Tailor series approach were deduced and reported. Performance is evaluated and examined with others related estimators considered using empirical study utilized two natural populations and simulated data sets. The statistical package R plus is used for computations. However, Results eventually indicated the superiority of proposed estimators over existing traditional estimators mentioned in studied.
Keywords: Auxiliary variable, dual to ratio-product-cum type, ratio-product-cum type, stratum, stratified random sampling, study variable, optimum values