By Sarjinder Singh (auth.)
This e-book is a multi-purpose record. it may be used as a textual content by way of academics, as a reference guide by way of researchers, and as a realistic consultant via statisticians. It covers 1165 references from diversified learn journals via virtually 1900 citations throughout 1194 pages, numerous entire proofs of theorems, vital effects reminiscent of corollaries, and 324 unsolved workouts from a number of study papers. It comprises 159 solved, data-based, actual existence numerical examples in disciplines resembling Agriculture, Demography, Social technology, utilized Economics, Engineering, medication, and Survey Sampling. those solved examples are very helpful for an realizing of the functions of complicated sampling thought in our lifestyle and in various fields of technological know-how. an extra 173 unsolved sensible difficulties are given on the finish of the chapters. college and school professors could locate those important while assigning workouts to scholars. every one workout provides publicity to numerous whole study papers for researchers/students.
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Additional info for Advanced Sampling Theory with Applications: How Michael ‘ selected’ Amy Volume I
2 CONSISTENCY There are several definitions for the consiste ncy of any statistic, but we will use the simplest. An estimator 0/ of the population parameter () is said to be consistent if Lim(O/)= o. 6) n-too For example: ( i ) The sample mean y/ ( or simply y) is a consis tent estimator of the finite popul ation mean, Y. ( ii ) The sample mean squared error s; is a consistent estimator of the population mean squared error , s;. 2. , the sample mean based on a sample of size one is unbiased but not consistent.
1 DI SCRETE RANDOM VA RIABLE If Xi is a discrete random variable with probability mass function distribution function, F(x )= p[X s x]= I P (Xi ) . i :xi ::;'x Let 0 ~ P( Xi) and F(x) ~ I be any random numb er drawn from the Pseudo-Random Number (PRN) Table I given in the Appendix. 1) Then the integr al value of the random variable x selected in the samp le is given by X=P-I[F(X) -. 2) where P - I denotes the inverse functio n. 30. 1. A discrete random variab le X has the followi ng probability mass function: Select a random sample of three units using the method of random numbers .
N ' =1 16 s =1 16 16 =- " Then we have the following new term . 1 BIAS It is the difference between the expected value of a statistic ()/ and the actual value of the parameter () that is B(O/) = £(0,)-o. 5) is unbi ased if £(0/)=(), which is obvious by setting B(OJ=o. 2 CONSISTENCY There are several definitions for the consiste ncy of any statistic, but we will use the simplest. An estimator 0/ of the population parameter () is said to be consistent if Lim(O/)= o. 6) n-too For example: ( i ) The sample mean y/ ( or simply y) is a consis tent estimator of the finite popul ation mean, Y.
Advanced Sampling Theory with Applications: How Michael ‘ selected’ Amy Volume I by Sarjinder Singh (auth.)