Estimation of the location parameter of distributions with known coefficient of variation by record values

N. K. Sajeevkumar, M. R. Irshad

Abstract


In this article, we derived the Best Linear Unbiased Estimator (BLUE) of the location parameter of certain distributions with known coefficient of variation by record values. Efficiency comparisons are also made on the proposed estimator with some of the usual estimators.     Finally we give a real life data to explain the utility of results developed in this article.

Keywords


Record values; Normal distribution; Logistic distribution; Exponential distribution; Best linear unbiased estimator

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References


M. AHSANULLAH (1995). Record Statistics, Nova Science Publishers, Commack, New York.

B. C. ARNOLD, N. BALAKRISHNAN, H. N. NAGARAJA (1998). Records, John Wiley and Sons, New York.

N. BALAKRISHNAN, P. S. CHAN (1998). On the normal record values and associated inference, Statistics and Probability Letters, 39, pp. 73-80.

N. BALAKRISHNAN, A. C. COHEN (1991). Order Statistics and Inference: Estimation Methods, San Diego, Academic Press.

K. BHAT, K. A. RAO (2011). Inference for Normal Mean with known Coefficient of Variation: Comparison using Simulation and Real Examples, Lap Lambert Academic Publishing GmbH and Co. KG.

K. N. CHANDLER (1982). The distribution and frequency of record values, Journal of Royal Statistical Society, Series B, 14, pp. 220-228.

H. A. DAVID (1981). Order Statistics, Second Edition, John Wiley and Sons, New York.

J. EEKELENS (1968). A method of calculation for logistic curve, Statistica Neerlandica, 22, pp. 213-217.

Y. FU, H. WANG, A. WONG (2013). Inference for the normal mean with known coefficient of variation, Open Journal of Statistics, 3, pp. 45-51.

M. GHOSH, A. RAZMPOUR (1982). Estimating the location parameter of an exponential distribution with known coefficient of variation, Calcutta Statistical Association Bulletin, 31, pp. 137-150.

L. J. GLESER, J. D. HEALY (1976). Estimating the mean of a normal distribution with known coefficient of variation, Journal of the American Statistical Association, 71, pp. 977-981.

N. GLICK (1978). Breaking records and breaking boards, Amer. Math. Monthly., 85, pp. 2-26.

H. GUO, N. PAL (2003). On a normal mean with known coefficient of variation, Calcutta Statistical Association Bulletin, 54, pp. 17-29.

B. R. HANDA, N. S. KAMBO, C.D. RAVINDRAN (2002). Testing of scale parameter of the exponential distribution with known coefficient of variation: conditional approach, Communications in Statistics-Theory and Methods, 31, pp. 73-86.

S. HEDAYAT, B. K. SINHA, W. ZHANG. (2011). Some aspects of inference on a normal mean with known coefficient of variation, International Journal of Statistical Science, 11, pp. 159-181.

A. M. KAGAN, Y. MALINOVSKY (2013). On the Nile problem by Sir Ronald Fisher, Electronic Journal of Statistics, 7, pp. 1968-1982.

R. A. KHAN (2013). A remark on estimating the mean of a normal distribution with known coefficient of variation, Statistics: A Journal of Theoretical and Applied Statistics, pp. 1-7.

S. KUNTE (2000). A Note on consistent maximum likelihood estimation for N(θ; θ2) family, Calcutta Statistical Association Bulletin, 50, PP. 325-328.

J. E. LAWLESS (1982). Statistical Models and Methods of Lifetime Data, John Wiley and Sons, New York.

W. B. NELSON (1990). Accelerated Testing: Statistical Models, Test Plans and Data Analysis, John Wiley and Sons, New York.

S. I. RESNICK (1973). Limit laws for record values, Stochastic Processes and Their Applications, 1, pp. 67-82.

E. M. ROBERTS (1979). Review of statistics of extreme values with applications to air quality data, Journal of the Air Pollution Control Association, 29, pp. 733-740.

N. K. SAJEEVKUMAR, P. Y. THOMAS (2005). Estimating the mean of logistic distribution with known coefficient of variation by order statistics, Recent Advances in Statistical Theory and Applications, ISPS proceedings 1, pp. 170-176.

N. K. SAJEEVKUMAR, M. R. IRSHAD (2011). Estimating the parameter of the exponential distribution with known coefficient of variation using censored sample by order statistics, IAPQR Transactions, 36, pp. 155-169.

N. K. SAJEEVKUMAR, M. R. IRSHAD (2012). Estimation of the mean of the double exponential distribution with known coefficient of variation by U-Statistics, Journal of the Kerala Statistical Association, 23, pp. 61-71.

N. K. SAJEEVKUMAR, M. R. IRSHAD (2013A). Estimating the parameter of the exponential distribution with known coefficient of variation by order statistics, Aligarh Journal of Statistics, 33, pp. 22-32.

N. K. SAJEEVKUMAR, M. R. IRSHAD (2013B). Estimation of the mean of the normal distribution with known coefficient of variation by U-Statistics, IAPQR, Transactions, 38, pp. 51-65.

D. T. SEARLS, P. INTARAPANICH (1990). A note on an estimator for the variance that utilizes kurtosis, The American Satistician, 44, pp. 295-296.

R .W. SHORROCK (1973). Record values and inter-record times, Journal of Applied Probability, 10, pp. 543-555.

P. Y. THOMAS, N. K. SAJEEVKUMAR (2003). Estimating the mean of normal distribution with known coefficient of variation by order statistics, Journal of the Kerala Statistical Association, 14, pp. 26-32.




DOI: 10.6092/issn.1973-2201/5308