Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 2 , pp. 227--237

NONUNIFORM SPEED OF CONVERGENCE TO NORMALITY WHILE SAMPLING FROM FINITE POPULATION

By

RATAN DASGUPTA, *Indian Statistical Institute*

SUMMARY. The speed of convergence to central limit theorem are studied under appropriate assumptions on the moment of population as the population size increases. As the consequences of nonuniform rates, probabilities of the deviations are computed. Some moment type convergences are proved for standardised sample sum to that of a standard normal variable. A nonuniform L_{p} version of the Berry-Esseen theorem is also established.

*AMS subject classification.* 60F99.

*Key words and phrases.* Non uniform $L_p$ version of Berry-Esseen theorem, moderate deviation.