Related Research Articles
In statistics,the Kolmogorov–Smirnov test is a nonparametric test of the equality of continuous,one-dimensional probability distributions that can be used to test whether a sample came from a given reference probability distribution,or to test whether two samples came from the same distribution. Intuitively,the test provides a method to qualitatively answer the question "How likely is it that we would see a collection of samples like this if they were drawn from that probability distribution?" or,in the second case,"How likely is it that we would see two sets of samples like this if they were drawn from the same probability distribution?". It is named after Andrey Kolmogorov and Nikolai Smirnov.
Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability. Inferential statistical analysis infers properties of a population,for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.
Andrey Nikolaevich Kolmogorov was a Soviet mathematician who contributed to the mathematics of probability theory,topology,intuitionistic logic,turbulence,classical mechanics,algorithmic information theory and computational complexity.
Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional,rather than finite dimensional,as is parametric statistics. Nonparametric statistics can be used for descriptive statistics or statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are evidently violated.
Minimum message length (MML) is a Bayesian information-theoretic method for statistical model comparison and selection. It provides a formal information theory restatement of Occam's Razor:even when models are equal in their measure of fit-accuracy to the observed data,the one generating the most concise explanation of data is more likely to be correct. MML was invented by Chris Wallace,first appearing in the seminal paper "An information measure for classification". MML is intended not just as a theoretical construct,but as a technique that may be deployed in practice. It differs from the related concept of Kolmogorov complexity in that it does not require use of a Turing-complete language to model data.
In mathematics,integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. In more recent times,the meaning has been broadened to include a view of invariant transformations from the space of functions on one geometrical space to the space of functions on another geometrical space. Such transformations often take the form of integral transforms such as the Radon transform and its generalizations.
Per Erik Rutger Martin-Löf is a Swedish logician,philosopher,and mathematical statistician. He is internationally renowned for his work on the foundations of probability,statistics,mathematical logic,and computer science. Since the late 1970s,Martin-Löf's publications have been mainly in logic. In philosophical logic,Martin-Löf has wrestled with the philosophy of logical consequence and judgment,partly inspired by the work of Brentano,Frege,and Husserl. In mathematical logic,Martin-Löf has been active in developing intuitionistic type theory as a constructive foundation of mathematics;Martin-Löf's work on type theory has influenced computer science.
The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measures can be used in statistical hypothesis testing,e.g. to test for normality of residuals,to test whether two samples are drawn from identical distributions,or whether outcome frequencies follow a specified distribution. In the analysis of variance,one of the components into which the variance is partitioned may be a lack-of-fit sum of squares.
In statistics,the Lilliefors test is a normality test based on the Kolmogorov–Smirnov test. It is used to test the null hypothesis that data come from a normally distributed population,when the null hypothesis does not specify which normal distribution;i.e.,it does not specify the expected value and variance of the distribution. It is named after Hubert Lilliefors,professor of statistics at George Washington University.
The Shapiro–Wilk test is a test of normality. It was published in 1965 by Samuel Sanford Shapiro and Martin Wilk.
In statistics,normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed.
In 1973,Andrey Kolmogorov proposed a non-probabilistic approach to statistics and model selection. Let each datum be a finite binary string and a model be a finite set of binary strings. Consider model classes consisting of models of given maximal Kolmogorov complexity. The Kolmogorov structure function of an individual data string expresses the relation between the complexity level constraint on a model class and the least log-cardinality of a model in the class containing the data. The structure function determines all stochastic properties of the individual data string:for every constrained model class it determines the individual best-fitting model in the class irrespective of whether the true model is in the model class considered or not. In the classical case we talk about a set of data with a probability distribution,and the properties are those of the expectations. In contrast,here we deal with individual data strings and the properties of the individual string focused on. In this setting,a property holds with certainty rather than with high probability as in the classical case. The Kolmogorov structure function precisely quantifies the goodness-of-fit of an individual model with respect to individual data.
The following is a timeline of probability and statistics.
Minimum-distance estimation (MDE) is a conceptual method for fitting a statistical model to data,usually the empirical distribution. Often-used estimators such as ordinary least squares can be thought of as special cases of minimum-distance estimation.
A plot is a graphical technique for representing a data set,usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a computer. In the past,sometimes mechanical or electronic plotters were used. Graphs are a visual representation of the relationship between variables,which are very useful for humans who can then quickly derive an understanding which may not have come from lists of values. Given a scale or ruler,graphs can also be used to read off the value of an unknown variable plotted as a function of a known one,but this can also be done with data presented in tabular form. Graphs of functions are used in mathematics,sciences,engineering,technology,finance,and other areas.
This page lists articles related to probability theory. In particular,it lists many articles corresponding to specific probability distributions. Such articles are marked here by a code of the form (X:Y),which refers to number of random variables involved and the type of the distribution. For example (2:DC) indicates a distribution with two random variables,discrete or continuous. Other codes are just abbreviations for topics. The list of codes can be found in the table of contents.
Nikolai Vasilyevich Smirnov was a Soviet Russian mathematician noted for his work in various fields including probability theory and statistics.
References
- 1 2 3 "SelectedWorks - Harry J. Khamis". works.bepress.com.
- 1 2 J.Khamis, Harry (August 22, 2011). The Association Graph and the Multigraph for Loglinear Models. SAGE Publications, Inc. doi:10.4135/9781452226521. ISBN 9781412972383 – via methods.sagepub.com.
- 1 2 "Many Honored at Presidential Address, Awards Ceremony | Amstat News". October 1, 2014.
- ↑ "Faculty and Staff Directory | Department of Mathematics and Statistics | College of Science & Mathematics | Wright State University". science-math.wright.edu.
- ↑ "Predicting Adult Stature Without Using Skeletal Age: The Khamis-Roche Method - Erratum appears in following issue".
- ↑ Khamis, H. J.; Guo, Shumei (August 22, 1993). "Improvement in the Roche-Wainer-Thissen stature prediction model: A comparative study". American Journal of Human Biology. 5 (6): 669–679. doi:10.1002/ajhb.1310050609. PMID 28548358. S2CID 38501384 – via CrossRef.
- ↑ Ranasinghe, Chathuranga; Gamage, Prasanna; Katulanda, Prasad; Andraweera, Nalinda; Thilakarathne, Sithira; Tharanga, Praveen (2013). "Relationship between Body Mass Index (BMI) and body fat percentage, estimated by bioelectrical impedance, in a group of Sri Lankan adults: a cross sectional study". BMC Public Health. 13. doi: 10.1186/1471-2458-13-797 . PMC 3766672 . PMID 24004464.
- ↑ Bullock, John D.; Elder, B. Laurel; Khamis, Harry J.; Warwar, Ronald E. (February 14, 2011). "Effects of Time, Temperature, and Storage Container on the Growth of Fusarium Species: Implications for the Worldwide Fusarium Keratitis Epidemic of 2004-2006". Archives of Ophthalmology. 129 (2): 133–136. doi:10.1001/archophthalmol.2010.338. PMID 21320955 – via Silverchair.
- ↑ Khamis, H. J. (June 22, 1997). "The delta-corrected Kolmogorov-Smirnov test for the two-parameter Weibull distribution". Journal of Applied Statistics. 24 (3): 301–318. Bibcode:1997JApSt..24..301K. doi:10.1080/02664769723701 – via CrossRef.
- ↑ Khamis, H. J. (1987). "On Buffon's Needle Problem Using Concentric Circles". Pi Mu Epsilon Journal. 8 (6): 368–376. JSTOR 24337919.