Improved estimation of the scale parameter for log-logistic  distribution using balanced ranked set sampling

Housila P. Singh; Vishal  Mehta

doi:https://doi.org/10.59170/stattrans-2017-003

Improved estimation of the scale parameter for log-logistic distribution using balanced ranked set sampling

Housila P. Singh School of Studies in Statistics, Vikram University, Ujjain - 456010, Madhya Pradesh, India. , Vishal Mehta Indian Statistical Institute (ISI), North-East Centre, Tezpur - 784028, Assam, India. Statistics in Transition new series, vol. 18, 2017, 1, pages: 53-74 Published online: 1 March 2017 https://doi.org/10.59170/stattrans-2017-003

138 Views 9 Downloads

ARTICLE

(English) PDF

ABSTRACT

In this article we have suggested some improved estimators of a scale parameter of log-logistic distribution (LLD) under a situation where the units in a sample can be ordered by judgement method without any error. We have also suggested some linear shrinkage estimator of a scale parameter of LLD. Efficiency comparisons are also made in this work.

KEYWORDS

minimum mean squared error estimator, shrinkage estimator, log-logistic distribution, best linear unbiased estimator, median ranked set sample

REFERENCES

AHMAD, M. I., SINCLAIR, C. D., WERRITTY, A., (1988). Log-logistic flood frequency analysis. J Hydrol, 98, pp. 205–224.

BALAKRISHNAN, N., MALIK, H. J., (1987). Best linear unbiased estimation of location and scale parameter of the log-logistic distribution. Commun Stat Theory Methods, 16, pp. 3477–3495.

BENNETT, S., (1983). Log-logistic regression models for survival data. J R Stat Soc, Ser C 32, pp. 165–171.

CHEN, Z., BAI, Z., SINHA, B. K., (2004). Ranked set sampling, theory and applications. Lecture Notes in Statistics, Springer, New York.

FISK, P. R., (1961). The graduation of income distributions. Econometrica, 29,pp. 171–185.

GESKUS, R. B., (2001). Methods for estimating the AIDS incubation time distribution when data of seroconversion is censored. Stat Med, 20, 795–812.

LESITHA, G., THOMAS, P. Y., (2012). Estimation of the scale parameter of A LOG-LOGISTICS DISTRIBUTION. METRIKA, DOI 10.1007/S00184-012-0397-5.

MCINTYRE, G. A., (1952). A method for unbiased selective sampling using ranked sets. Aust J Agric Res, 3, pp. 385–390.

MEHTA, V., (2015). Estimation in Morgenstern Type Bivariate Exponential Distribution with Known Coefficient of Variation by Ranked Set Sampling. Proceeding of the “30th M. P. Young Scientist Congress” (MPYSC-2015), M. P. Council of Science and Technology, Vigyan Bhawan, Nehru Nagar, Bhopal -462 003, Madhya Pradesh, India.

MEHTA, V., SINGH, H. P., (2014). Shrinkage Estimators of Parameters of Morgenstern Type Bivariate Logistic Distribution Using Ranked Set Sampling. Journal of Basic and Applied Engineering Research (JBAER), 1 (13), pp. 1–6.

MUTTLAK, H. A., (1997). Median ranked set sampling. J Appl Stat Sci. 6, pp. 245–255.

RAGAB, A., GREEN, J., (1984). On order statistics from the log-logistic distribution and their properties. Commun Stat Theory Methods, 13, pp. 2713–2724.

ROBSON, A., REED, D., (1999). Flood estimation handbook, 3. Statistical procedures for flood frequency estimation. Institute of Hydrology, Wallingford, UK.

SHOUKRI, M. M., MIAN, I. U. M., TRACY, D., (1988). Sampling properties of estimators of log-logistic distribution with application to Canadian precipitation data. Can J Stat, 16, pp. 223–236.

SINGH, H. P., MEHTA, V., (2013). An Improved Estimation of Parameters of Morgenstern Type Bivariate Logistic Distribution Using Ranked Set Sampling. STATISTICA, 73 (4), pp. 437–461.

SINGH, H. P., MEHTA, V., (2016a). Improved Estimation of Scale Parameter of Morgenstern Type Bivariate Uniform Distribution Using Ranked Set Sampling. Communications in Statistics – Theory and Methods, 45 (5),pp. 1466–1476.

SINGH, H. P., MEHTA, V., (2014a). Linear shrinkage estimator of scale parameter of Morgenstern type bivariate logistic distribution using ranked set sampling. Model Assisted Statistics and Applications (MASA), 9, pp. 295–307.

SINGH, H. P., MEHTA, V., (2014b). An Alternative Estimation of the Scale Parameter for Morgenstern Type Bivariate Log-Logistic Distribution Using Ranked Set Sampling. Journal of Reliability and Statistical Studies, 7 (1), pp. 19–29.

SINGH, H. P., MEHTA, V., (2015). Estimation of Scale Parameter of a Morgenstern Type Bivariate Uniform Distribution Using Censored Ranked Set Samples. Model Assisted Statistics and Applications (MASA), 10, pp. 139–153.

SINGH, H. P., MEHTA, V., (2016b). Some Classes of Shrinkage Estimators in the Morgenstern Type Bivariate Exponential Distribution Using Ranked Set Sampling. Hacettepe Journal of Mathematics and Statistics, 45 (2), pp. 575–591.

SINGH, H. P., MEHTA, V., (2016c). A Class of Shrinkage Estimators of Scale Parameter of Uniform Distribution Based on K- Record Values. National Academy Science Letters, 39, pp. 221–227.