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Estimation of Finite Population Mean in Multivariate Stratified Sampling under Cost Function Using Goal Programming

Author

Listed:
  • Atta Ullah
  • Javid Shabbir
  • Zawar Hussain
  • Bander Al-Zahrani

Abstract

In practical utilization of stratified random sampling scheme, the investigator meets a problem to select a sample that maximizes the precision of a finite population mean under cost constraint. An allocation of sample size becomes complicated when more than one characteristic is observed from each selected unit in a sample. In many real life situations, a linear cost function of a sample size nh is not a good approximation to actual cost of sample survey when traveling cost between selected units in a stratum is significant. In this paper, sample allocation problem in multivariate stratified random sampling with proposed cost function is formulated in integer nonlinear multiobjective mathematical programming. A solution procedure is proposed using extended lexicographic goal programming approach. A numerical example is presented to illustrate the computational details and to compare the efficiency of proposed compromise allocation.

Suggested Citation

  • Atta Ullah & Javid Shabbir & Zawar Hussain & Bander Al-Zahrani, 2014. "Estimation of Finite Population Mean in Multivariate Stratified Sampling under Cost Function Using Goal Programming," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:686579
    DOI: 10.1155/2014/686579
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    References listed on IDEAS

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    1. Romero, Carlos, 2001. "Extended lexicographic goal programming: a unifying approach," Omega, Elsevier, vol. 29(1), pages 63-71, February.
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