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Author: K. Carolynne Ayienda
Publisher: BoD – Books on Demand
ISBN: 3732267237
Category : Mathematics
Languages : en
Pages : 162
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Book Description
The gamma distribution is one of the continuous distributions. Gamma distributions are very versatile and give useful presentations of many physical situations. They are perhaps the most applied statistical distribution in the area of reliability. Gamma distributions are of different types, 1, 2, 3, 4-parameters. They are applied in different fields, among them finance, economics, hydrological and in civil engineering. In this study we have constructed different types of gamma distributions using transformation/change of variable and cumulative techniques and calculated their properties using moments, identified their special cases and calculated their properties too. We have also constructed gamma related distribution using transformation and cumulative techniques and most of these distributions are expressed using special functions, also we have used the gamma-generator and gamma exponetiated–generator to generate new family of distributions.
Author: K. Carolynne Ayienda
Publisher: BoD – Books on Demand
ISBN: 3732267237
Category : Mathematics
Languages : en
Pages : 162
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Book Description
The gamma distribution is one of the continuous distributions. Gamma distributions are very versatile and give useful presentations of many physical situations. They are perhaps the most applied statistical distribution in the area of reliability. Gamma distributions are of different types, 1, 2, 3, 4-parameters. They are applied in different fields, among them finance, economics, hydrological and in civil engineering. In this study we have constructed different types of gamma distributions using transformation/change of variable and cumulative techniques and calculated their properties using moments, identified their special cases and calculated their properties too. We have also constructed gamma related distribution using transformation and cumulative techniques and most of these distributions are expressed using special functions, also we have used the gamma-generator and gamma exponetiated–generator to generate new family of distributions.
Author: Lennart Bondesson
Publisher: Springer Science & Business Media
ISBN: 1461229480
Category : Mathematics
Languages : en
Pages : 184
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Book Description
Generalized Gamma convolutions were introduced by Olof Thorin in 1977 and were used by him to show that, in particular, the Lognormal distribution is infinitely divisible. After that a large number of papers rapidly appeared with new results in a somewhat random order. Many of the papers appeared in the Scandinavian Actuarial Journal. This work is an attempt to present the main results on this class of probability distributions and related classes in a rather logical order. The goal has been to be on a level that is not too advanced. However, since the field is rather technical, most readers will find difficult passages in the text. Those who do not want to visit a mysterious land situated between the land of probability theory and statistics and the land of classical analysis should not look at this work. When some years ago I submitted a survey to a journal it was suggested by the editor, K. Krickeberg, that it should be expanded to a book. However, at that time I was rather reluctant to do so since there remained so many problems to be solved or to be solved in a smoother way than before. Moreover, there was at that time some lack of probabilistic interpretations and applications. Many of the problems are now solved but still it is felt that more applications than those presented in the work could be found.
Author: Bowman
Publisher: CRC Press
ISBN: 9780824775568
Category : Mathematics
Languages : en
Pages : 294
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Book Description
Author: Gerald J. Hahn
Publisher: Wiley-Interscience
ISBN: 9780471040651
Category : Mathematics
Languages : en
Pages : 0
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Book Description
A detailed treatment on the use of statistical models representing physical phenomena. Considers the relevance of the popular normal distribution models and the applicability of exponential distribution in reliability problems. Introduces and discusses the use of alternate models such as gamma, beta and Weibull distributions. Features expansive coverage of system performance and describes an exact method known as the transformation of variables. Deals with techniques on assessing the adequacy of a chosen model including both graphical and analytical procedures. Contains scores of illustrative examples, most of which have been adapted from actual problems.
Author: Luc Devroye
Publisher: Springer Science & Business Media
ISBN: 1461386438
Category : Mathematics
Languages : en
Pages : 859
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Book Description
Thls text ls about one small fteld on the crossroads of statlstlcs, operatlons research and computer sclence. Statistleians need random number generators to test and compare estlmators before uslng them ln real l fe. In operatlons research, random numbers are a key component ln arge scale slmulatlons. Computer sclen tlsts need randomness ln program testlng, game playlng and comparlsons of algo rlthms. The appl catlons are wlde and varled. Yet all depend upon the same com puter generated random numbers. Usually, the randomness demanded by an appl catlon has some bullt-ln structure: typlcally, one needs more than just a sequence of Independent random blts or Independent uniform 0,1] random vari ables. Some users need random variables wlth unusual densltles, or random com blnatorlal objects wlth speclftc propertles, or random geometrlc objects, or ran dom processes wlth weil deftned dependence structures. Thls ls preclsely the sub ject area of the book, the study of non-uniform random varlates. The plot evolves around the expected complexlty of random varlate genera tlon algorlthms. We set up an ldeal zed computatlonal model (wlthout overdolng lt), we lntroduce the notlon of unlformly bounded expected complexlty, and we study upper and lower bounds for computatlonal complexlty. In short, a touch of computer sclence ls added to the fteld. To keep everythlng abstract, no tlmlngs or computer programs are lncluded. Thls was a Iabor of Iove. George Marsagl a created CS690, a course on ran dom number generat on at the School of Computer Sclence of McG ll Unlverslty."
Author: Ben Lambert
Publisher: SAGE
ISBN: 1526418266
Category : Social Science
Languages : en
Pages : 738
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Book Description
Supported by a wealth of learning features, exercises, and visual elements as well as online video tutorials and interactive simulations, this book is the first student-focused introduction to Bayesian statistics. Without sacrificing technical integrity for the sake of simplicity, the author draws upon accessible, student-friendly language to provide approachable instruction perfectly aimed at statistics and Bayesian newcomers. Through a logical structure that introduces and builds upon key concepts in a gradual way and slowly acclimatizes students to using R and Stan software, the book covers: An introduction to probability and Bayesian inference Understanding Bayes′ rule Nuts and bolts of Bayesian analytic methods Computational Bayes and real-world Bayesian analysis Regression analysis and hierarchical methods This unique guide will help students develop the statistical confidence and skills to put the Bayesian formula into practice, from the basic concepts of statistical inference to complex applications of analyses.
Author: Philip J. Boland
Publisher: CRC Press
ISBN: 158488696X
Category : Business & Economics
Languages : en
Pages : 368
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Book Description
Statistical and Probabilistic Methods in Actuarial Science covers many of the diverse methods in applied probability and statistics for students aspiring to careers in insurance, actuarial science, and finance. The book builds on students' existing knowledge of probability and statistics by establishing a solid and thorough understanding of
Author: Aerospace Research Laboratories (U.S.)
Publisher:
ISBN:
Category : Probabilities
Languages : en
Pages : 272
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Book Description
Author: Nabendu Pal
Publisher: CRC Press
ISBN: 0203490282
Category : Mathematics
Languages : en
Pages : 370
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Book Description
The normal distribution is widely known and used by scientists and engineers. However, there are many cases when the normal distribution is not appropriate, due to the data being skewed. Rather than leaving you to search through journal articles, advanced theoretical monographs, or introductory texts for alternative distributions, the Handbook of E
Author: Tomasz J. Kozubowski
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
There is considerable literature on matrix-variate gamma distributions, also known as Wishart distributions, which are driven by a shape parameter with values in the (Gindikin) set {i/2, i = 1, . . . , k-1}∪((k-1)/2, ∞). We provide an extension of this class to the case where the shape parameter may actually take on any positive value. In addition to the well-known singular Wishart as well as non-singular matrix-variate gamma distributions, the proposed class includes new singular matrix-variate distributions, with the shape parameter outside of the Gindikin set. This singular, non-Wishart case is no longer permutation invariant and derivation of its scaling properties requires special care. Among numerous newly established properties of the extended class are group-like relations with respect to the positive shape parameter. The latter provide a natural substitute for the classical convolution properties that are crucial in the study of infinite divisibility. Our results provide further clarification regarding the lack of infinite divisibility of Wishart distributions, a classical observation of Paul L'evy. In particular, we clarify why the row/column vectors in the off-diagonal blocks are infinitely divisible. A class of matrix-variate Laplace distributions arises naturally in this set-up as the distributions of the off-diagonal blocks of random gamma matrices. For the class of Laplace rectangular matrices, we obtain distributional identities that follow from the role they play in the structure of the matrix gamma distributions. We present several elegant and convenient stochastic representations of the discussed classes of matrix-valued distributions. In particular, we show that the matrix-variate gamma distribution is a symmetrization of the triangular Rayleigh distributed matrix - a new class of the matrix variables that naturally extend the classical univariate Rayleigh variables. Finally, a connection of the matrix-variate gamma distributions to matrix-valued L'evy processes of a vector argument is made. Namely, a L'evy process, termed a matrix gammaLaplace motion, is obtained by the subordination of the triangular Brownian motion of a vector argument to a vector-valued gamma motion of a vector argument. In this context, we introduce a triangular matrix-valued Rayleigh process, which, through symmetrization, leads to a new matrix-variate gamma process. This process when taken at a properly defined one-dimensional argument has the matrix gamma marginal distribution with the shape parameter equal to its argument.
