DOI Prefix : 10.9780 | Journal DOI : 10.9780/22307850
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Volume : IV, Issue : V, June - 2014

MODIFIED RATIO TYPE ESTIMATOR OF TWO POPULATION MEANS IN STRATIFIED SAMPLING

Rafia Jan, S. Maqbool Aquil Ahmad Asra Nazir

DOI : 10.9780/22307850, By : Laxmi Book Publication

Abstract :

A modified ratio estimator is proposed for ratio of two population means using auxiliary information in stratified random sampling. Bias and mean square error expression are obtained and the proposed estimator is compared theoretically and empirically with classical estimator.

Keywords :


Article :


Cite This Article :

Rafia Jan, S. Maqbool Aquil Ahmad Asra Nazir (2014). MODIFIED RATIO TYPE ESTIMATOR OF TWO POPULATION MEANS IN STRATIFIED SAMPLING. Indian Streams Research Journal, Vol. IV, Issue. V, DOI : 10.9780/22307850, http://isrj.org/UploadedData/4846.pdf

References :

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  37. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
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  52. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  53. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  54. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
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  56. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
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  60. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  61. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  62. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  63. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  64. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  65. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  66. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
  67. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  68. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  69. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  70. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  71. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  72. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  73. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  74. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  75. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  76. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  77. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  78. population parameters. Sankhya, B, 27, 321-328.
  79. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  80. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  81. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  82. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  83. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
  84. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  85. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  86. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  87. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  88. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  89. population parameters. Sankhya, B, 27, 321-328.
  90. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
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  92. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  93. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  94. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  95. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  96. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  97. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  98. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  99. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  100. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  101. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  102. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  103. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  104. population parameters. Sankhya, B, 27, 321-328.
  105. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  106. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  107. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  108. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  109. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  110. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  111. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  112. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  113. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  114. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  115. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  116. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  117. population parameters. Sankhya, B, 27, 321-328.
  118. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  119. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  120. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  121. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  122. population parameters. Sankhya, B, 27, 321-328.
  123. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  124. population parameters. Sankhya, B, 27, 321-328.
  125. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  126. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  127. population parameters. Sankhya, B, 27, 321-328.
  128. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  129. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  130. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  131. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  132. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  133. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  134. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  135. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  136. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  137. population parameters. Sankhya, B, 27, 321-328.
  138. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  139. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  140. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  141. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  142. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  143. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  144. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  145. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  146. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  147. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  148. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  149. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  150. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  151. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  152. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  153. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  154. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  155. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  156. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  157. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  158. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  159. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  160. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  161. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  162. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  163. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
  164. population parameters. Sankhya, B, 27, 321-328.
  165. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  166. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  167. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  168. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  169. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  170. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  171. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  172. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  173. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  174. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  175. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  176. population parameters. Sankhya, B, 27, 321-328.
  177. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  178. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
  179. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  180. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  181. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  182. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  183. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  184. population parameters. Sankhya, B, 27, 321-328.
  185. population parameters. Sankhya, B, 27, 321-328.
  186. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  187. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  188. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  189. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  190. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  191. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  192. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  193. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  194. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  195. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  196. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  197. population parameters. Sankhya, B, 27, 321-328.
  198. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  199. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  200. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  201. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  202. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  203. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  204. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  205. population parameters. Sankhya, B, 27, 321-328.
  206. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  207. population parameters. Sankhya, B, 27, 321-328.
  208. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  209. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
  210. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
  211. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  212. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  213. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  214. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  215. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  216. population parameters. Sankhya, B, 27, 321-328.
  217. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  218. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  219. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  220. population parameters. Sankhya, B, 27, 321-328.
  221. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  222. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  223. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
  224. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  225. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  226. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  227. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  228. population parameters. Sankhya, B, 27, 321-328.
  229. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  230. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  231. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  232. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  233. population parameters. Sankhya, B, 27, 321-328.
  234. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  235. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  236. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  237. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  238. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  239. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  240. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  241. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  242. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  243. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  244. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  245. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  246. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  247. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  248. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  249. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  250. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  251. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  252. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  253. population parameters. Sankhya, B, 27, 321-328.
  254. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  255. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  256. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  257. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  258. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  259. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  260. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  261. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  262. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  263. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  264. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  265. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  266. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  267. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  268. population parameters. Sankhya, B, 27, 321-328.
  269. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  270. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  271. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  272. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  273. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  274. population parameters. Sankhya, B, 27, 321-328.
  275. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  276. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  277. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  278. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  279. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  280. population parameters. Sankhya, B, 27, 321-328.
  281. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  282. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  283. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  284. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  285. population parameters. Sankhya, B, 27, 321-328.
  286. population parameters. Sankhya, B, 27, 321-328.
  287. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  288. population parameters. Sankhya, B, 27, 321-328.
  289. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  290. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  291. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  292. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  293. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
  294. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  295. population parameters. Sankhya, B, 27, 321-328.
  296. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  297. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
  298. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  299. population parameters. Sankhya, B, 27, 321-328.
  300. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  301. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  302. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  303. population parameters. Sankhya, B, 27, 321-328.
  304. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  305. population parameters. Sankhya, B, 27, 321-328.
  306. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  307. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  308. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  309. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  310. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  311. population parameters. Sankhya, B, 27, 321-328.
  312. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  313. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  314. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  315. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  316. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  317. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  318. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  319. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  320. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  321. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  322. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  323. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  324. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  325. population parameters. Sankhya, B, 27, 321-328.
  326. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  327. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  328. population parameters. Sankhya, B, 27, 321-328.
  329. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  330. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  331. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  332. population parameters. Sankhya, B, 27, 321-328.
  333. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  334. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  335. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  336. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  337. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  338. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  339. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  340. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  341. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  342. population parameters. Sankhya, B, 27, 321-328.
  343. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
  344. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  345. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  346. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  347. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  348. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  349. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  350. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  351. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  352. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
  353. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  354. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  355. population parameters. Sankhya, B, 27, 321-328.
  356. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  357. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  358. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  359. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  360. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  361. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  362. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  363. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  364. Ray, S.K., & Singh, R.K. (1985). Some estimators for the ratio and product of
  365. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  366. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  367. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  368. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  369. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  370. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  371. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  372. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  373. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  374. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  375. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  376. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  377. population parameters. Sankhya, B, 27, 321-328.
  378. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
  379. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
  380. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  381. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  382. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  383. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  384. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  385. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  386. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  387. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  388. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  389. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  390. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  391. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  392. population parameters. Sankhya, B, 27, 321-328.
  393. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  394. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  395. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  396. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  397. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  398. population parameters. Sankhya, B, 27, 321-328.
  399. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  400. Murthy & Singh, M.P. (1965). On the estimation of ratio and product of the
  401. population parameters. Journal of the Indian Society of Agricultural Statistics, 37 (1), 1-10.
  402. proportion. Applied Mathematical Science, 3(35), 1739-1744.
  403. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  404. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  405. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  406. variable for estimating the ratio of two population means in sample surveys. Model Assisted. Statistics and Applications, 1(1), IOS Press, 1-5
  407. means and ratios using supplementary. Statistica. Neerlandica, 39(3), 309-318.
  408. Upadhyaya, L.N., Singh, H.P., & Vos, J.W.E. (1985). On the estimation of population
  409. Sindhu, S.S., Tailor, R., & Singh, S. (2009). On the estimation of population
  410. Singh, G.N., & Rani, R. (2005, 2006). Some linear transformations on auxiliary
  411. information for estimating ratio of two finite means. Gujarat Statistical Review, 12(2), 7-16.
  412. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio
  413. Upadhyaya, L.N., & Singh, H.P., (1985). A class of estimators using auxiliary
  414. (product) of two population parameters. Sankhya, C, 40 (2), 156-166.
  415. Rao, J.N.K., & Pereira, N.P. (1968). On double ratio estimators. Sankhya, A, 30, 83-90.
  416. Shah, S.M., & Shah, D.N. (1978). Ratio-cum-product estimator for estimating ratio

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