Probability, Statistics, and Stochastic Processes
... In November 2003, I was completing a review of an undergraduate textbook in probability and statistics. In the enclosed evaluation sheet was the question “Have you ever considered writing a textbook?” and I suddenly realized that the answer was “Yes,” and had been for quite some time. For several ye ...
... In November 2003, I was completing a review of an undergraduate textbook in probability and statistics. In the enclosed evaluation sheet was the question “Have you ever considered writing a textbook?” and I suddenly realized that the answer was “Yes,” and had been for quite some time. For several ye ...
Chapter 1: Probability models and counting
... Probability theory is the mathematical toolbox to describe phenomena or experiments where randomness occur. To have a probability model we need the following ingredients • A sample space S which is the collection of all possible outcomes of the (random) experiment. We shall consider mostly finite sa ...
... Probability theory is the mathematical toolbox to describe phenomena or experiments where randomness occur. To have a probability model we need the following ingredients • A sample space S which is the collection of all possible outcomes of the (random) experiment. We shall consider mostly finite sa ...
Statistical methods for detecting genotype - Til Daim
... the genetic marker. The methods are applied to simulated datasets in order to measure their test size and statistical power, and to compare them. Interaction between the genetic marker and the environmental effect is also considered, and strategies for simulating cohort and case-control data with ge ...
... the genetic marker. The methods are applied to simulated datasets in order to measure their test size and statistical power, and to compare them. Interaction between the genetic marker and the environmental effect is also considered, and strategies for simulating cohort and case-control data with ge ...
Empirical likelihood inference for two-sample problems Changbao Wu and Ying Yan
... with missing responses; (iv) bootstrap calibration procedures for the proposed weighted and pseudo empirical likelihood methods. Results from a limited simulation study showed that our proposed methods perform very well. The methods are also applied to a real data example on family expenditures. AMS ...
... with missing responses; (iv) bootstrap calibration procedures for the proposed weighted and pseudo empirical likelihood methods. Results from a limited simulation study showed that our proposed methods perform very well. The methods are also applied to a real data example on family expenditures. AMS ...
AP Stat 6.2
... We’ll learn about two commonly occurring discrete random variables: binomial random variables and geometric random variables. We’ll learn about Binomial Settings and Binomial Random Variables ...
... We’ll learn about two commonly occurring discrete random variables: binomial random variables and geometric random variables. We’ll learn about Binomial Settings and Binomial Random Variables ...
Package `homtest`
... (j) a sample of θAD , j = 1, . . . , Nsim values, whose empirical distribution function can be used as an approximation of GH0 (θAD ), the distribution of θAD under the null hypothesis of homogeneity. The acceptance limits for the test, corresponding to any significance level α, are then easily dete ...
... (j) a sample of θAD , j = 1, . . . , Nsim values, whose empirical distribution function can be used as an approximation of GH0 (θAD ), the distribution of θAD under the null hypothesis of homogeneity. The acceptance limits for the test, corresponding to any significance level α, are then easily dete ...
Statistics
Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or societal problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as ""all persons living in a country"" or ""every atom composing a crystal"". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.Two main statistical methodologies are used in data analysis: descriptive statistics, which summarizes data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draws conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and a synthetic data drawn from idealized model. An hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a ""false positive"") and Type II errors (null hypothesis fails to be rejected and an actual difference between populations is missed giving a ""false negative""). Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis.Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other important types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data and/or censoring may result in biased estimates and specific techniques have been developed to address these problems.Statistics can be said to have begun in ancient civilization, going back at least to the 5th century BC, but it was not until the 18th century that it started to draw more heavily from calculus and probability theory. Statistics continues to be an area of active research, for example on the problem of how to analyze Big data.