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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
11

The small-sample power of some nonparametric tests

Gibbons, Jean Dickinson January 1962 (has links)
I. Small-Sample Power of the One-Sample Sign Test for Approximately Normal Distributions. The power function of the one-sided, one-sample sign test is studied for populations which deviate from exact normality, either by skewness, kurtosis, or both. The terms of the Edgeworth asymptotic expansion of order more than N<sup>-3/2</sup> are used to represent the population density. Three sets of hypotheses and alternatives, concerning the location of (1) the median, (2) the median as approximated by the mean and coefficient of skewness, and (3) the mean, are considered in an attempt to make valid comparisons between the power of the sign test and Student's t test under the same conditions. Numerical results are given for samples of size 10, significance level .05, and for several combinations of the coefficients of skewness and kurtosis. II. Power of Two-Sample Rank Teats on the Equality of Two Distribution Functions. A comparative study is made of the power of two-sample rank tests of the hypothesis that both samples are drawn from the same population. The general alternative is that the variables from one population are stochastically larger than the variables from the other. One of the alternatives considered is that the variables in the first sample are distributed as the smallest of k variates with distribution F, and the variables in the second sample are distributed as the largest of these k – H₁ : H = 1 - (1 - F)<sup>k</sup>, G = F<sup>k</sup>. These two alternative distributions are mutually symmetric if F is symmetrical. Formulae are presented, which are independent of F, for the evaluation of the probability under H₁ of any joint arrangement of the variables from the two samples. A theorem is proved concerning the equality of the probabilities of certain pairs of orderings under assumptions of mutually symmetric populations. The other alternative is that both samples are normally distributed with the same variance but different means, the standardized difference between the two extreme distributions in the first alternative corresponding to the difference between the means. Numerical results of power are tabulated for small sample sizes, k = 2, 3 and 4, significance levels .01, .05 and .10. The rank tests considered are the most powerful rank test, the one and two-sided Wilcoxon tests, Terry's c₁ test, the one and two-aided median tests, the Wald-Wolfowitz runs test, and two new tests called the Psi test and the Gamma test. The two-sample rank test which is locally most powerful against any alternative·expressing an arbitrary functional relationship between the two population distribution functions and an unspecified parameter θ is derived and its asymptotic properties studied. The method is applied to two specific functional alternatives, H₁* : H = (1-θ)F<sup>k</sup> + θ[1 - (1-F)<sup>k</sup>], G = F<sup>k</sup>, and H₁**: H = 1 - (1-F)<sup>1+θ</sup>, G = F<sup>1+θ</sup>, where θ ≥ 0, which are similar to the alternative of two extreme distributions. The resulting test statistics are the Gamma test and the Psi test, respectively. The latter test is shown to have desirable small-sample properties. The asymptotic power functions of the Wilcoxon and WaldWolfowitz tests are compared for the alternative of two extreme distributions with k = 2, equal sample sizes and significance level .05. / Ph. D.
12

Estimation in truncated distributions

Furrow, Linda Joyce January 1968 (has links)
When some population values are completely from observation, the distribution from which the observations came is said to be truncated. Estimation of the parameters from truncated distributions has been an open field for research. This thesis examines the developments which have taken place in this area, giving the major writers and the methods used by them to obtain estimators. A. C. Cohen is responsible for much work involving the maximum likelihood procedure. Using the method of moments and several methods which they have developed, Rider, Plackett, Samford, Moore, Des Raj, and Halperin have made significant contributions. The Poisson, Normal, Binomial, Negative Binomial, and Gamma distributions are included in the investigation and along with the estimators, in some cases, asymptotic variances are given. Though much work has been done, there are many things left to be investigated. Only a small number of distributions have been dealt with, with all multivariate distributions other than the normal lacking any investigation. It is not known how the estimators are affected by small sample sizes, and with the aid of the computer variances can be examined. A new problem arises when the points of truncation are not clearly defined and complicated equations often make estimators difficult to fine. / M.S.
13

A power study of multiple range and multiple F tests

Wine, R. Lowell 12 January 2010 (has links)
In the study of multiple comparisons tests the following topics were discussed: (i) extension to the general case of certain properties and results which previously had been given for three and four means only, (ii) power vectors and average power, (iii) expressions of power for the multiple range tests and for the multiple F test involving only three means, and (iv) methods for evaluating power. These four topics are amplified in order in the four paragraphs below. A set of recursion formulas was obtained for enumerating the decision patterns for n means. x<sub>i</sub> was given by the equation See: Equation where i = 1, 2,...,n-1. In IV, formulas were derived which express d<sub>j,i+1</sub> as a function of the x<sub>i</sub>. This made possible the writing of the bounding equations for any decision region involving n means. The regions (1,2), (1,2,3), (1,2,4), ..., (1,2....,n) for the multiple range tests were described in the sample-space of differences among n means. / Ph. D.
14

A study of statistical and deterministic models for the prediction of the composition of a mixture

Myers, Raymond H. 07 April 2010 (has links)
This thesis is a study of various physical and statistical models which may be useful for the prediction of the composition of a ternary liquid mixture. The particular mixture considered in this study was the solvent system consisting of nitroglycerine (NG), 2-nitrodiphenylamine (2NDPA), and triacetin (TA). Several models were investigated for their adequacy and closeness of fit. An attempt has been made to relate the actual composition to a few easily measurable quantities, namely, refractive index, density, and the separate analysis of 2NDPA. Deterministic models relating the concentration of each component in the mixture with the physical determinations mentioned above have been considered first. These models are based on the known theory of physical chemistry. The deterministic model which was chosen as "best" in terms of the smallness of error of prediction, estimates the composition from the determination of density and the spectrophotometer analysis of 2NDPA. Since the latter analysis is a quick and accurate determination of the 2NDPA content and since the content of the third component could be determined by complementing to 100 percent, the models have been formulated in terms of the concentration of only one component, namely NG. The statistical models under investigation are divided into activity models and regression models. The activity model is a combination of chemical and statistical theory while the simple regression model represents an approach that a statistician might take if he disregarded the physical or chemical theory involved. Two activity models have been discussed, the first assuming the activity of the mixture constant and the second assuming the activity of the mixture to be a weighted sum of the activities of the three components. Tests of hypotheses are made to determine whether the activity models result in a significant reduction in error over that of the "best" deterministic model. The investigation that the model formulated assuming constant activity of the mixture results in the smallest error of estimation among all models under study. Thus it has been used as a basis for the preparation of control charts. The linear regression models, constructed with various functions of density, refractive index, and spectrophotometer analysis as independent variables, produced errors of estimation above those for the deterministic model. Chapter IV represents the summary of the thesis and the translation of findings into actual control charts. On the basis of this chapter, a technician can easily determine the estimate of the composition of the mixture and the attached 99 percent confidence bounds. Thus, this Chapter contains these charts combined with instructions in their use and numerical examples. / Master of Science
15

Sample and counting variations associated with x-ray flourescence [sic] analysis

Davis, Robert Loyal January 1966 (has links)
M. S.
16

Power characteristics of Kramer's method for analysis of variance of a two-way classification with disproportionate subclass numbers

Dunn, James Eldon January 1963 (has links)
A theorem by Shah and Khatri [A.M.S. (1961) 321883-887] is extended to give the distribution of Q/X² , where Q is a positive definite quadratic form involving non-central normal variates and X² is an independently distributed chi-square variate. Conditions are given under which the distribution of this ratio reduces to that of non-central F. Kramer’s method for analysis of variance of a two-way classification with disproportionate subclass numbers is reviewed and shown to satisfy these conditions. Various functional forms of the non-centrality parameter for evaluating the power of his method are given. Additional algebraic and numerical results are obtained to compare the power of Kramer's method and the method of fitting constants (least squares) outlined by Yates [J.A.S.A. (1934) 24151-66]. A mnemonic rule, based on 310 randomly generated two-way classifications, is given for discriminating against use of Kramer’s method in situations where his method potentially may be very deficient in power as compared to the method of fitting constants. / Ph. D.
17

Seismicity Analyses Using Dense Network Data : Catalogue Statistics and Possible Foreshocks Investigated Using Empirical and Synthetic Data

Adamaki, Angeliki January 2017 (has links)
Precursors related to seismicity patterns are probably the most promising phenomena for short-term earthquake forecasting, although it remains unclear if such forecasting is possible. Foreshock activity has often been recorded but its possible use as indicator of coming larger events is still debated due to the limited number of unambiguously observed foreshocks. Seismicity data which is inadequate in volume or character might be one of the reasons foreshocks cannot easily be identified. One method used to investigate the possible presence of generic seismicity behavior preceding larger events is the aggregation of seismicity series. Sequences preceding mainshocks chosen from empirical data are superimposed, revealing an increasing average seismicity rate prior to the mainshocks. Such an increase could result from the tendency of seismicity to cluster in space and time, thus the observed patterns could be of limited predictive value. Randomized tests using the empirical catalogues imply that the observed increasing rate is statistically significant compared to an increase due to simple clustering, indicating the existence of genuine foreshocks, somehow mechanically related to their mainshocks. If network sensitivity increases, the identification of foreshocks as such may improve. The possibility of improved identification of foreshock sequences is tested using synthetic data, produced with specific assumptions about the earthquake process. Complications related to background activity and aftershock production are investigated numerically, in generalized cases and in data-based scenarios. Catalogues including smaller, and thereby more, earthquakes can probably contribute to better understanding the earthquake processes and to the future of earthquake forecasting. An important aspect in such seismicity studies is the correct estimation of the empirical catalogue properties, including the magnitude of completeness (Mc) and the b-value. The potential influence of errors in the reported magnitudes in an earthquake catalogue on the estimation of Mc and b-value is investigated using synthetic magnitude catalogues, contaminated with Gaussian error. The effectiveness of different algorithms for Mc and b-value estimation are discussed. The sample size and the error level seem to affect the estimation of b-value, with implications for the reliability of the assessment of the future rate of large events and thus of seismic hazard. / Οι προσεισμοί αποτελούν τα πλέον υποσχόμενα πρόδρομα φαινόμενα για τη βραχυπρόθεσμη πρόγνωση των σεισμών, παρόλο που παραμένει άγνωστο το αν μια τέτοια πρόγνωση είναι εφικτή. Η χρήση της προσεισμικής δραστηριότητας ως ένδειξη ενός επερχόμενου μεγάλου σεισμού είναι αμφιλεγόμενη, κυρίως λόγω του περιορισμένου πλήθους των προσεισμών, γεγονός που πιθανά οφείλεται στην ανεπαρκή καταγραφή σεισμικών δεδομένων. Η άθροιση σεισμικών σειρών είναι μια μέθοδος που εφαρμόζεται προκειμένου να μελετηθεί η πιθανή παρουσία ενός γενικευμένου μοτίβου σεισμικότητας πριν από ισχυρούς σεισμούς. Η υπέρθεση σεισμικών ακολουθιών που προηγήθηκαν των κυρίων σεισμών αναδεικνύει μια αυξανόμενη μέση δραστηριότητα πριν από τους κύριους σεισμούς. Μια τέτοια συμπεριφορά θα μπορούσε να προκύψει και από την εγγενή τάση των σεισμών να ομαδοποιούνται χωρικά και χρονικά, με αποτέλεσμα τα παρατηρούμενα μοτίβα να έχουν περιορισμένη προγνωστική αξία. Τυχαιοποιημένοι έλεγχοι των πραγματικών δεδομένων υποδηλώνουν ότι ο παρατηρούμενος αυξανόμενος ρυθμός είναι στατιστικά σημαντικός σε σύγκριση με τη μεταβολή που οφείλεται στη γένεση απλών συστάδων σεισμών, αναδεικνύοντας την ύπαρξη προσεισμών αιτιολογικά συσχετιζόμενων με τους κύριους σεισμούς. Μια ενδεχόμενη αύξηση της ευαισθησίας των σεισμικών δικτύων πιθανά να συμβάλει στην αποτελεσματικότερη αναγνώριση των προσεισμών. Η πιθανότητα μιας τέτοιας βελτίωσης ελέγχεται με τη χρήση συνθετικών δεδομένων τα οποία προκύπτουν υπό προϋποθέσεις ως προς τη σεισμική διαδικασία. Οι επιπλοκές που μπορεί να προκύψουν από την παρουσία σεισμικότητας υποβάθρου και των μετασεισμικών ακολουθιών διερευνώνται αριθμητικά, με γενικευμένες περιπτώσεις και σενάρια που βασίζονται σε πραγματικά δεδομένα. Οι κατάλογοι που περιλαμβάνουν μικρότερους και επομένως περισσότερους σεισμούς μπορούν πιθανώς να συμβάλουν στην καλύτερη κατανόηση των σεισμικών διεργασιών και στη μελλοντική πρόγνωση των σεισμών. Σημαντική πτυχή σε τέτοιες μελέτες αποτελεί η σωστή εκτίμηση των ιδιοτήτων των σεισμικών καταλόγων, όπως είναι το μέγεθος πληρότητας και η παράμετρος b. Η επίδραση των σφαλμάτων των μεγεθών που υπάρχουν στους σεισμικούς καταλόγους στην εκτίμηση των προαναφερθέντων ιδιοτήτων ερευνάται χρησιμοποιώντας συνθετικά μεγέθη στα οποία ενυπάρχουν κανονικώς κατανεμημένα σφάλματα. Κατά τη διερεύνηση της αποτελεσματικότητας των διαφόρων μεθόδων που χρησιμοποιούνται για την εκτίμηση του μεγέθους πληρότητας προκύπτει ότι το μέγεθος του δείγματος και του σφάλματος των μεγεθών μπορούν να επηρεάσουν την εκτίμηση της παραμέτρου b, με επιπτώσεις στην εκτίμηση του ρυθμού των μελλοντικών ισχυρών σεισμών και την αξιολόγηση του σεισμικού κινδύνου.
18

Almost sure behavior for increments of U-statistics / Beschreibung der Fluktuation von Zuwächsen für U-Statistiken

Abujarad, Mohammed 18 January 2007 (has links)
No description available.
19

A PHENOMENOLOGICAL STUDY OF MATHEMATICS TEACHER EDUCATORS¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿ EXPERIENCES RELATED TO AND PERCEPTIONS OF STATISTICS

Hogue, Mark D. 11 December 2012 (has links)
No description available.
20

OPTICAL PROPERTIES AND POPULATION STATISTICS OF ERBIUM IN OPTICALLY-PUMPED ERBIUM-DOPED ZINC SILICATE GERMANATE WAVEGUIDE AMPLIFIERS

BANERJEE, SIDDHARTHA January 2004 (has links)
No description available.

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