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Articles 181 - 195 of 195
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On A General Class Of Unbiased Ratio, Product, Ratio-Cum-Product And Regression Type Estimators., N. S. Sastry Dr.
On A General Class Of Unbiased Ratio, Product, Ratio-Cum-Product And Regression Type Estimators., N. S. Sastry Dr.
Doctoral Theses
Probability enmpling methods ha ve extenaive a pplication in la rge- eca le agricultural and socio economic surve ys, Sampling is ale used in one or more stages of a census and sometimes as a mubstitute for a complete Census. Over the pa st four deca de s, confidence in the use of san pling and a ppreciation for the technique have stee dily grown thanks to the pi onee ring efforts of Neyman, Hansen, Hurwit z, Maha lanobis, Sukha tme, Cochran, Yate s and others.2. It is well known that the principa i problem of the theory of sampling …
Some Combinatorial Arrangements And Incomplete Block Designs Through Them., Anis Chandra Mukherjee Dr.
Some Combinatorial Arrangements And Incomplete Block Designs Through Them., Anis Chandra Mukherjee Dr.
Doctoral Theses
The use and importance, in Statistical Experimental, of Incomplete Block Designs, particularly, Balanced Incomplete Block (BIB) Designs, Doubly Balanced Incomplete Block (DBIB) Designs and Partially Balanced Inçomplete Block (PBIB) Designs are well known. Several combinational arrangements, including the incidence matrices of these Incomplete Block Designs and association matrices associated with PBIB Designs are known to be of use in Design of Experiments. In this thesis, we consider the construction problems pertaining to some of these combinational arrangements and take up the problem of construction of BIB, DBIB and FBIB Designs through them. The combinational arrangements studied in the thesis have, …
Some Contribution To The Theory Applications And Computations Of Generalized Inverses Of Matrices., Pochiraju Bhimasankaram Dr.
Some Contribution To The Theory Applications And Computations Of Generalized Inverses Of Matrices., Pochiraju Bhimasankaram Dr.
Doctoral Theses
The origin of the concept of a generalized inverse dates back to as early as 1920 when Moore defined the generalized inverse of matrix which is equivalent toDefinition 1 (Moore) : Let A be a m >< n matrix over the field of complex numbers. Then a is the generalized Inverse of A if AG is the orthogonal projection operator projecting arbitrary vectors onto the column space of A and GA is the orthogonal projection operator projecting arbitrary sectors onto, the column space of G.Mod re (1935) discussed this concept and its properties in some detail. Tsong (1949a, 1949b, 1956) discussed about generalized 1nverses of operators in more general spaces and Bjerhammer (1951) discussed the generalized inverse of a matrix in connection with an application to geodetic calculations. Unaware of the work of Hoore and others, Penrose (1955) defined a generalized inverse of a matrix as follows :Definition 2 (Penrosel) : Let A be a m *n -matrix over the field of complex numbers. Then G is a generalized inverse of a if (i) AFA= A; (ii) GAG=G; (iii) (AG)*=AG and (iv) (GA)*-GA.Penrose (1955,1956) showed that for every matrix there exists a unique generalized inverse, discussed several of its important properties, gave applications to solution of matrix equations and suggested a practical method of computation of the generalised inverse.As was pointed out by Rado (1956) Moo res definition of generalized inverse is equivalent to that of Penrose, Such generalized inverse is called the Moore-Penrose inverse and A is used to denote the Moore-Penrose inverse of A.Rao (1955), unaware of the earlier or contemporary Work, constructed a pseudo-inverse of a matrix which he used in some least squares computations, In a paper in 1962, he defined a generalized inverse (g-inverse) as follows, proved some interesting properties and gave applications of g-inverses to Mathomatical Statistics.Definition 3 (Rao) : Lot A be am x n matrix, Then a n >< m matrix. Then a n >< m matrix G is a g-inverse of A if x = Gy is a solution of the linear system Ax = y whenever it is consistent.A g-inverse if u matrix (in the sense of Rao) is in general not unique, As 1s easily observed (from definitions 2 and 4) the class of all g-inverses of a matrix A contains A*. Rạo (1965, 1967) developed a calculus of g-inverses, classified the g-inverses according to their use and according to the proporties they possess similar to those of the inverse of a nonsingular matrix and suggested further applications to Mathematical Statistics. Mitra (1968a, 1968b) gave an equivalem definition of a g-inverse, developed further calculus of z-inverses, used g-invorses to solve some matrix equations of interest and explored the possibilities of some new classes of g-inverses with applications. In a series of papers, and a monograph Mitra and Rao (1968, 1970) pursued the research on generalized inverses of matrix's and their applications to various scientific disciplines.
A New Confidence Interval For The Mean Of A Normal Distribution, David Lee Wallace
A New Confidence Interval For The Mean Of A Normal Distribution, David Lee Wallace
All Master's Theses
A typical problem in statistical inference is the following: An experimenter is confronted with a density function f(x; ϴ) which describes the underlying population of measurements. The form of f may or may not be known, and ϴ is a parameter (possibly vector-valued) which describes the population. The statistician's job is to estimate or to test hypotheses about the unknown parameter ϴ. In this paper, we shall consider interval estimation of the mean of the normal density function.
Optimum Estimators And Strategies In Survey Sampling., M. K. Ramakrishnan Dr.
Optimum Estimators And Strategies In Survey Sampling., M. K. Ramakrishnan Dr.
Doctoral Theses
This thesis consists of nine chapters. In the first chapter we give the basic concepts and definitions and also a broad review of the literature related to the problems considered in this thesis. The second and third chapters are devoted to a detailed modified comparison of sampling with and without replacement, for the case of equal and unequal probability sampling respectively. In the fourth and fifth chapters we discuss the criteria of hyper-admissibility and linear suf2iciency for the choice of an optimum estimator for a given sampling design. The succeeding three chapters have as their main objective the central problem …
Some Statistical Considerations On Population Structure, Genetic Correlation And Human Multiple Births., Ranajit Chakraborty Dr.
Some Statistical Considerations On Population Structure, Genetic Correlation And Human Multiple Births., Ranajit Chakraborty Dr.
Doctoral Theses
Siree the reiiecovery of Mentel'a works tamsrds tha beglaning of this contury the mnetiolete did not confine their atudies only at fanilial level. The atudy of penetie entities at poyulation level also bocune equally important for understending the mol.ani an of inharitanec. Thda branch of urderotanding the neoahantes of herodity, knowa sa Population Geneties, has by noe bacane no eli incm that a discunoion of say part of it drea not nead ny geneeal introtuetion. In view of shia faot, we irstead speni sone time to get into the problans diseussus in this thesia.Bastcally wa atudy theeo problene in this …
Theory Of Equitable Quality Level And Errors- Areas Under The Operating Characteristic Curves Of Lot Acceptance Sampling Plans., M. T. Subramanya Dr.
Theory Of Equitable Quality Level And Errors- Areas Under The Operating Characteristic Curves Of Lot Acceptance Sampling Plans., M. T. Subramanya Dr.
Doctoral Theses
This monograph deals with the theory of Equitable Quality Level and error-areas under the operating characte- ristic curves of lot acceptance sampling plans. A brief sumnary of the contents is given in Sections 1.2b (pages 15-16) and 2.9 (pages 107-111). A fairly good idea of the topics considored in this monograph can be obtained from the detailod list of contents given in pagos iv- xi.Most of the results given in the monograph are new and have not been published anywhe re. They are based on author's own research work and are contained in his doctoral dissertation.Most of the work connected …
Some Contributions To The Analysis Of Circular Data., J. S. Rao Dr.
Some Contributions To The Analysis Of Circular Data., J. S. Rao Dr.
Doctoral Theses
In many diverae scientifie fields, one cones serose experimente where the basie variable unter obaervation ia a direction. We ahall be conoerned, throughout this theais, only with diraations in two-dimensions and wo refer to such a collection of directione an 'circular data or dimenstionl data. In order to make a statintical analyaie of circular data, the first prerequisite is to put thom in a quantitative form. One way of doing thie is to represent the directiona anglea no aaured d thre apeet to eone mui tably choscn sero direation. Al ternately, einee a direetion han no nagni- tude, it can …
Some Stochastic Models In Reliability., R. Natarajan Dr.
Some Stochastic Models In Reliability., R. Natarajan Dr.
Doctoral Theses
The work presented in this thesis was carried out under the supervision of Dr. J. Sethuraman, Research & Training School, Indian Statistical Institute, Calcutta, and is devoted to the study of some stochastic models of standby and parallel redundant systems. Some of the reliability characteristics studied are the expected time to system failure, the long-run availability, expected number of system failures in a given interval of time, interval reliability etc. These reliability characteristics will be useful in the better design of systems and making management decisions in improving system reliability.The investigations carried out in this thesis are presented in four …
Threshold Order Of A Switching Function And Stochastic Dependence Of Inputs., T. Krishnan Dr.
Threshold Order Of A Switching Function And Stochastic Dependence Of Inputs., T. Krishnan Dr.
Doctoral Theses
This Ä‘insertation is being submitted to the Indian Statiatical Inatitute, in support of the author's application for the degree of Doctor of Philosophy. This diasertation enbodien the work carried out by the author at the Indian Statistieal Institute under the aupervision of frofensor C. R. Rso. le is grate ful to Professor Rao for his constant encouragenent and inspi- ration and for the facilities provided at the Institute.The main part of the results of Chapter 5 have already been ublished (20). Zhe resulte of Chapters 2 and 3 and of Chapter 4 &e being reviewed for publie cation. ReferRes of …
Some Statistical Studies On Languages., Nikhilesh Bhattacharya Dr.
Some Statistical Studies On Languages., Nikhilesh Bhattacharya Dr.
Doctoral Theses
The investigations reported in the present the is were started towards the end of 1957 and carried along internittently amidst teaching and professnional work on ample surveys and econometrics, Curiosity provided the major inpulse. The authors ambition was, initially, to throw up sone numerical tubles for Benguli, Sanskrit, Prakrit and Pali, such usüre found for many western languages in Herdans (1956) Language as Choice and Chance. Grudually, as the work progressed, the view changed and more analytical studies suggested themselves. Some of the se latter have been completed in arrovidional manner and re ported in the present thesis.Chapter 1 attempts …
Simulation Of Mathematical Models In Genetic Analysis, Dinesh Govindal Patel
Simulation Of Mathematical Models In Genetic Analysis, Dinesh Govindal Patel
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
In recent years a new field of statistics has become of importance in many branches of experimental science. This is the Monte Carlo Method, so called because it is based on simulation of stochastic processes. By stochastic process, it is meant some possible physical process in the real world that has some random or stochastic element in its structure. This is the subject which may appropriately be called the dynamic part of statistics or the statistics of "change," in contrast with the static statistical problems which have so far been the more systematically studied. Many obvious examples of such processes …
Convolution Properties Of Distributions On Topological Groups., S. R. S. Varadhan Dr.
Convolution Properties Of Distributions On Topological Groups., S. R. S. Varadhan Dr.
Doctoral Theses
The collection of probability distributions on the real line which is a semigroup under the convolution operation and topological space under weak convergence has attracted, during the last quarter of a century, the attention of such great mathematicians as Khintchine, Kolmogorov, Bawly, Levy and others. Their results constitute a deep analysis of the factorization problems on the one hand and the asymptotic behavior of infinite convolutions on the other. However, a complete and systematic investigation of these problems is not available in considerable generality. The aim of the present thesis is to investigate the topological and algebraic properties and the …
Distribution Theory Of Some Classification Statistics., S. John Dr.
Distribution Theory Of Some Classification Statistics., S. John Dr.
Doctoral Theses
This thesis eives the distri bution theory of four clae aifioation statistics. Sone parta of it were published a few years ago. The relevant publicationa are listed nt the end.What the author knows of related work by other authors is set out in the Introductions little material of this nature is given elsewhere in the theats. If a result is not explicitly credited to another author, it may be taken to nean that the author believes it to be hia worik.It will be noticed that three (U, R and 2) of the four statistics receive less a pace than the …
Some Results Concerning Asymptotic Distributions And Their Applications., J. Sethuraman Dr.
Some Results Concerning Asymptotic Distributions And Their Applications., J. Sethuraman Dr.
Doctoral Theses
This thesis is being submitted to the Indian statistical Institute in support of the author's application for the degree of doctor of philosophy. The thesis embodies research carried out by the author during the period 1958-1961 under the supervision of dr.R.R. Bahadur, Professor of statistics are the Indian Statistical Institute Calcutta.This thesis is concerned with development of a new method of establishing asymptotic distributions and the elaboration of some of its applications in several fields of statistics.The thesis consists of five chapters. Chapter I describes, in general terms, the various problems considered in the thesis. Chapter II Deals with the …