Estimating the Variance of an Exponential Distribution in the Presence of Large True Observations

Authors

  • Housila P. Singh School of Studies in Statistics, Vikram University, Ujjain, India
  • Vankim Chander School of Studies in Statistics, Vikram University, Ujjain, India

DOI:

https://doi.org/10.17713/ajs.v37i2.301

Abstract

The present paper discusses some classes of shrinkage estimators for the variance of the exponential distribution in the presence of large true observations when some a priori or guessed interval containing the variance parameter is available from some past experiences. Empirical study shows the high efficiency of the developed classes of shrinkage estimators when compared with Pandey and Singh’s estimator, minimum MSE estimator and special classes of shrinkage estimators.

References

Bartholomew, D. J. (1957). A problem of life testing. Journal of the American Statistical Association, 65, 350-355.

Jani, P. N. (1991). A class of shrinkage estimators for the scale parameter of the exponential distribution. IEEE Transactions on Reliability, 40, 68-70.

Mehta, J. S., and Srinivasan, R. (1971). Estimation of the mean by shrinkage to a point. Journal of the American Statistical Association, 66, 86-90.

Ojha, V. P. (1982). A note on estimation of variance in exponential density. Journal of the Indian Society of Agricultural Statistics, 34, 82-88.

Ojha, V. P., and Srivastava, S. R. (1979). An estimator of the population variance in the presence of large true observations. Journal of the Indian Society of Agricultural

Statistics, 31, 77-84.

Pandey, B. N., and Singh, J. (1977). A note on estimation of variance in exponential density. Sankhya, B, 39, 294-298.

Saxena, S. (2006). A decision theoretic estimation in exponential product life testing model using guesstimate. Vikalpa, 31, 31-45.

Saxena, S., and Singh, H. P. (2004). Estimating various measures in normal population through a single class of estimators. Journal of the Korean Statistical Society, 33,

-337.

Saxena, S., and Singh, H. P. (2006). From ordinary to shrinkage square-root estimators. Communications in Statistics – Theory and Methods, 35, 1037-1058.

Searls, D. T. (1966). An estimators for a population mean which reduces the effect of large true observations. Journal of the American Statistical Association, 59, 1200-1204.

Singh, H. P. (1987). A modified estimator for normal population variance in the presence of large true observations. Gujarat Statistical Review, 14, 15-30.

Singh, H. P., and Chander, V. (2007). Some classes of shrinkage estimators for estimating the scale parameter towards an interval of exponential distribution. Journal of

Probability and Statistical Science. (accepted)

Singh, H. P., and Saxena, S. (2003). An improved class of shrinkage estimators for the variance of a normal population. Statistics in Transition, 6, 119-129.

Singh, H. P., and Saxena, S. (2005). Using prior information in estimation of kth exponent of scale parameter in negative exponent population. Statistical Methods, 7, 116-126.

Singh, H. P., Saxena, S., and Espejo, M. R. (2004). Estimation of standard deviation in normal parent by shrinkage towards an interval. Journal of Statistical Planning and Inference, 126, 479-493.

Singh, H. P., and Shukla, S. K. (2002). A class of shrinkage estimators for the variance of exponential distribution with type-I censoring. Indian Association for Productivity,

Quality and Reliability Transactions, 27, 119-141.

Srivastava, R. S. (1986). On estimation of mean life time from a time censored sample using exponential failure model. Journal of National Academy of Mathematics,

India, 4, 107-113.

Srivastava, R. S., and Kumar, G. (1990). Efficient estimation of variance of exponential population in the presence of large true observations. Journal of National Academy of Mathematics, India, 8, 61-71.

Srivastava, R. S., Pandey, B. N., and Srivastava, S. R. (1985). A modified estimator for the population mean which reduces the effect of large true observations. Journal of the Indian Society of Agricultural Statistics, 37, 71-78.

Thompson, J. R. (1968). Accuracy borrowing in the estimation of mean by shrinkage to an interval. Journal of the American Statistical Association, 63, 113-122.

Tracy, D. S., Singh, H. P., and Raghuvanshi, H. S. (1996). Some shrinkage estimator for the variance of exponential density. Microelectron Reliability, 36, 651-655.

Upadhyaya, L. N., Gangele, R. K., and Singh, H. P. (1997). A shrinkage estimator for the scale parameter of the exponential distribution with type-I censoring. International

Journal of Management System, 13, 103-114.

Downloads

Published

2016-04-03

Issue

Section

Articles

How to Cite

Estimating the Variance of an Exponential Distribution in the Presence of Large True Observations. (2016). Austrian Journal of Statistics, 37(2), 207–216. https://doi.org/10.17713/ajs.v37i2.301