Thesis (M.A.) in Mathematics--University of Maine, 2008. / Includes vita. Includes bibliographical references (leaf 34).

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Η παρούσα μεταπτυχιακή διατριβή εντάσσεται ερευνητικά στην περιοχή της Στατιστικής Θεωρίας Αποφάσεων και ειδικότερα στη βελτίωση των εκτιμητών του μέτρου της διασποράς για την αντίστροφη κανονική κατανομή IG(μ,λ), όπου μ είναι η παράμετρος θέσης, ενώ το λ είναι η παράμετρος κλίμακος και εκφράζει το αντίστροφο μέτρο της διασποράς. Στο Κεφάλαιο 1 παρουσιάζονται κάποιοι χρήσιμοι, για την πορεία της μελέτης μας, ορισμοί και θεωρήματα, στο Κεφάλαιο 2 μελετάται το μοντέλο της αντίστροφης κανονικής κατανομής, δίνονται τα χαρακτηριστικά μεγέθη αυτής και υπολογίζονται γνωστοί εκτιμητές για το μέτρο της διασποράς. Στο Κεφάλαιο 3, εξετάζεται το πρόβλημα εκτίμησης του μέτρου της διασποράς , τόσο ως προς την τετραγωνική συνάρτηση ζημίας , όσο και προς την συνάρτηση ζημίας εντροπίας . Υπό ορισμένες συνθήκες, αποδεικνύεται η μη αποδεκτικότητα, του βέλτιστου αναλλοίωτου εκτιμητή, κατασκευάζοντας καλύτερους εκτιμητές τύπου Stein [1964, Ann. Inst. Statist. Math.]. Η μέθοδος κατασκευής αυτών των εκτιμητών παρουσιάστηκε στην εργασία των N. Pal and B. Sinha [1989, Statistical data analysis and inference]. Στο Κεφάλαιο 4, και για το ίδιο πρόβλημα εκτίμησης που πραγματεύεται το προηγούμενο κεφάλαιο,κατασκευάζονται καλύτεροι εκτιμητές από το βέλτιστο αναλλοίωτο εκτιμητή χρησιμοποιώντας την μεθοδολογία των Brewster and Zidek [1974, Ann. Statist.]. Η μέθοδος κατασκευής αυτών των εκτιμητών παρουσιάζεται στην εργασία των B.MacGibbon and G.Shorrock [1997, Statist. Probab. Lett.]. / The present postgraduate thesis is placed among the area of Statistical Decision Theory and especially we give improved estimators of dispersion of an inverse Gaussian distribution IG(μ,λ), where μ is the mean and λ is a parameter, known as inverse measure of dispersion. In Chapter 1 are some useful definitions and theorems are presented, in Chapter 2 the model of inverse Gaussian distribution is studied, we give some properties of the model and known estimators for the measure of dispersion , are presented. In Chapter 3, we examine the problem of estimating the measure of dispersion under quadratic and entropy losses. Under certain conditions, we derive improved estimators (Stein [1964, Ann. Inst. Statist. Math.]) of the best affine equivariant estimator for . The method of construction of these estimators is presented in the paper of N. Pal and B. Sinha [ 1989, Statistical data analysis and inference ]. In Capital 4, and for the same problem of estimating , improved estimators of the best affine equivariant estimator are derived, using the methodology of Brewster and Zidek [1974, Ann. Statist. ]. This method of construction of these estimators is presented in the paper of B. MacGibbon and G. Shorrock [1997, Statist. Probab. Lett. ].

Statistical quality control (SQC) is one technique companies are using in the development of a Total Quality Management (TQM) culture. Shewhart control charts, a widely used SQC tool, rely on an underlying normal distribution of the data. Often data are skewed. The inverse Gaussian distribution is a probability distribution that is wellsuited to handling skewed data. This analysis develops models and a set of tools usable by practitioners for the constrained economic statistical design of control charts for inverse Gaussian distribution process centrality and process dispersion. The use of this methodology is illustrated by the design of an x-bar chart and a V chart for an inverse Gaussian distributed process.

by Wong Kwok Keung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 50-52). / Chapter 1. --- Introduction --- p.1 / Chapter 2. --- Taguchi's methodology in design of experiments --- p.3 / Chapter 2.1 --- System design / Chapter 2.2 --- Parameter design / Chapter 2.3 --- Tolerance design / Chapter 3. --- Inverse Gaussian distribution --- p.8 / Chapter 3.1 --- Genesis / Chapter 3.2 --- Probability density function / Chapter 3.3 --- Estimation of parameters / Chapter 3.4 --- Applications / Chapter 4. --- Iterative procedures and Derivation of the GLIM 4 macros --- p.21 / Chapter 4.1 --- Generalized linear models with varying dispersion / Chapter 4.2 --- Mean and dispersion models for inverse Gaussian distribution / Chapter 4.3 --- Devising the GLIM 4 macro / Chapter 4.4 --- Model fitting / Chapter 5. --- Simulation Study --- p.34 / Chapter 5.1 --- Generating random variates from the inverse Gaussian distribution / Chapter 5.2 --- Simulation model / Chapter 5.3 --- Results / Chapter 5.4 --- Discussion / Appendix --- p.46 / References --- p.50

Thesis (M. Sc. (Mathematical Statistics)) -- University of the North, 1978 / Refer to the document

Thesis (M.Eng.)--Memorial University of Newfoundland, 2003. / Bibliography: leaves 71-74. Also available online.

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<p>We discuss the Normal inverse Gaussian (NIG) distribution in modeling volatility in the financial markets. Refining the work of Barndorff-Nielsen (1997) and Andersson (2001), we introduce a new parameterization of the NIG distribution to build the GARCH(p,q)-NIG model. This new parameterization allows the model to be a strong GARCH in the sense of Drost and Nijman (1993). It also allows us to standardized the observed returns to be i.i.d., so that we can use standard inference methods when we evaluate the fit of the model.</p><p>We use the realized volatility (RV), calculated from intraday data, to standardize the returns of the ECU/USD foreign exchange rate. We show that normality cannot be rejected for the RV-standardized returns, i.e., the Mixture-of-Distributions Hypothesis (MDH) of Clark (1973) holds. {We build a link between the conditional RV and the conditional variance. This link allows us to use the conditional RV as a proxy for the conditional variance. We give an empirical justification of the GARCH-NIG model using this approximation.</p><p>In addition, we introduce a new General GARCH(p,q)-NIG model. This model has as special cases the Threshold-GARCH(p,q)-NIG model to model the leverage effect, the Absolute Value GARCH(p,q)-NIG model, to model conditional standard deviation, and the Threshold Absolute Value GARCH(p,q)-NIG model to model asymmetry in the conditional standard deviation. The properties of the maximum likelihood estimates of the parameters of the models are investigated in a simulation study.</p>

We discuss the Normal inverse Gaussian (NIG) distribution in modeling volatility in the financial markets. Refining the work of Barndorff-Nielsen (1997) and Andersson (2001), we introduce a new parameterization of the NIG distribution to build the GARCH(p,q)-NIG model. This new parameterization allows the model to be a strong GARCH in the sense of Drost and Nijman (1993). It also allows us to standardized the observed returns to be i.i.d., so that we can use standard inference methods when we evaluate the fit of the model. We use the realized volatility (RV), calculated from intraday data, to standardize the returns of the ECU/USD foreign exchange rate. We show that normality cannot be rejected for the RV-standardized returns, i.e., the Mixture-of-Distributions Hypothesis (MDH) of Clark (1973) holds. {We build a link between the conditional RV and the conditional variance. This link allows us to use the conditional RV as a proxy for the conditional variance. We give an empirical justification of the GARCH-NIG model using this approximation. In addition, we introduce a new General GARCH(p,q)-NIG model. This model has as special cases the Threshold-GARCH(p,q)-NIG model to model the leverage effect, the Absolute Value GARCH(p,q)-NIG model, to model conditional standard deviation, and the Threshold Absolute Value GARCH(p,q)-NIG model to model asymmetry in the conditional standard deviation. The properties of the maximum likelihood estimates of the parameters of the models are investigated in a simulation study.