Testing the Convenience of a Variate for Stratification in Estimating the Gini-Simpson Diversity

作者: María Carmen Alonso , María Angeles Gil

DOI: 10.1007/BFB0035952

关键词: Measure (mathematics)StatisticsStratification (mathematics)Stratified samplingPopulationMathematicsSimple random sampleRandom variateDelta methodDiversity (business)

摘要: In the literature on quantification of diversity in a population, one indices that has been proven to be useful dealing with uncensused populations is Gini-Simpson one. On other hand, whose respect certain aspect required quantified, often arise naturally stratified and large samples from them are available. Targets this paper are: approximate optimum allocation estimating sampling so asymptotic precision maximized; introduce relative gain (with allocation) over random as measure adequacy variate for stratification approximating diversity; construct procedure test convenience given samples.

参考文章(15)
H. Heyer, Information and Sufficiency Springer, New York, NY. pp. 142- 173 ,(1982) , 10.1007/978-1-4613-8218-8_7
G. P. Patil, C. Taillie, Diversity as a Concept and its Measurement Journal of the American Statistical Association. ,vol. 77, pp. 548- 561 ,(1982) , 10.1080/01621459.1982.10477845
María Angeles Gil, Pedro Gil, A procedure to test the suitability of a factor for stratification in estimating diversity Applied Mathematics and Computation. ,vol. 43, pp. 221- 229 ,(1991) , 10.1016/0096-3003(91)90007-A
Francois Bourguignon, Decomposable Income Inequality Measures Econometrica. ,vol. 47, pp. 901- 920 ,(1979) , 10.2307/1914138
K. Zografos, K. Ferentinos, T. Papaioannou, Divergence statistics: sampling properties and multinomial goodness of fit and divergence tests Communications in Statistics-theory and Methods. ,vol. 19, pp. 1785- 1802 ,(1990) , 10.1080/03610929008830290
Iapan Kumar Nayak, On diversity measures based on entropy functions Communications in Statistics-theory and Methods. ,vol. 14, pp. 203- 215 ,(1985) , 10.1080/03610928508828905
D. V. Lindley, On a Measure of the Information Provided by an Experiment Annals of Mathematical Statistics. ,vol. 27, pp. 986- 1005 ,(1956) , 10.1214/AOMS/1177728069
Maria Angeles Gil, A note on stratification and gain in precision in estimating diversity from large samples Communications in Statistics-theory and Methods. ,vol. 18, pp. 1521- 1526 ,(1989) , 10.1080/03610928908829983
C. Radhakrishna Rao, Diversity: its measurement, decomposition, apportionment and analysis Indian Statistical Institute. ,(1982)