Statistical characterization of stationary ergodic random signals
... Stationarity is the property of a random process which guarantees that its statistical properties, such as the mean value, its moments and variance, will not change over time. A stationary process is one whose probability distribution is the same at all times. A stochastic process is said to be ergo ...
... Stationarity is the property of a random process which guarantees that its statistical properties, such as the mean value, its moments and variance, will not change over time. A stationary process is one whose probability distribution is the same at all times. A stochastic process is said to be ergo ...
1 A simple example
... The problem for statistics is determining the value of this parameter p. All we know is that it lies between 0 and 1. We also expect the ratio k/n of the number of successes k to the number trials n to approach p as n approaches ∞, but that’s a theoretical result that doesn’t say much about what p i ...
... The problem for statistics is determining the value of this parameter p. All we know is that it lies between 0 and 1. We also expect the ratio k/n of the number of successes k to the number trials n to approach p as n approaches ∞, but that’s a theoretical result that doesn’t say much about what p i ...
Probability and Statistics - Digital Learning Department
... Decide if a specified model is consistent with results from a given datagenerating process (such as a simulation). ...
... Decide if a specified model is consistent with results from a given datagenerating process (such as a simulation). ...
PPT - Bioinformatics.ca
... • Used to determine if 2 populations are different • Formally allows you to calculate the probability that 2 sample means are the same • If the t-Test statistic gives you a p=0.4, and the a is 0.05, then the 2 populations are the same • If the t-Test statistic gives you a p=0.04, and the a is 0.05, ...
... • Used to determine if 2 populations are different • Formally allows you to calculate the probability that 2 sample means are the same • If the t-Test statistic gives you a p=0.4, and the a is 0.05, then the 2 populations are the same • If the t-Test statistic gives you a p=0.04, and the a is 0.05, ...
Statistical Testing 1 - Louisiana Tech University
... This is used to test the hypothesis that the data you are working with fits a given distribution. For example, if you want to determine whether the times of occurrence of meteorites during the Leonid meteor shower are inconsistent with a Poisson distribution, you could formulate the null hypothesis ...
... This is used to test the hypothesis that the data you are working with fits a given distribution. For example, if you want to determine whether the times of occurrence of meteorites during the Leonid meteor shower are inconsistent with a Poisson distribution, you could formulate the null hypothesis ...
Uses of Probabilities in Epidemiology Research
... We already have some idea where the middle of this “population curve” fits on a number line because we have the (ONE) sample estimate of that point; we are just not 100% confident that the sample statistic is exactly the same as the population parameter. What we need to know is the range of possible ...
... We already have some idea where the middle of this “population curve” fits on a number line because we have the (ONE) sample estimate of that point; we are just not 100% confident that the sample statistic is exactly the same as the population parameter. What we need to know is the range of possible ...
Chapter 2
... The correct way to round or report an intermediate value would be 278.05 rather than 278.1. The subscript indicates that one additional digit is retained to avoid rounding error. The additional digit does not change the count of significant digits: The value 278.05 still has four significant digits. ...
... The correct way to round or report an intermediate value would be 278.05 rather than 278.1. The subscript indicates that one additional digit is retained to avoid rounding error. The additional digit does not change the count of significant digits: The value 278.05 still has four significant digits. ...
Notes are listed
... A stochastic process (or just a process) is a collection of random variables X (t ) for certain values of t. In this class we will consider only non-negative values t ≥ 0. The process is a continuous-time process if all non-negative values of t are allowed; that is, if there is a random variable ...
... A stochastic process (or just a process) is a collection of random variables X (t ) for certain values of t. In this class we will consider only non-negative values t ≥ 0. The process is a continuous-time process if all non-negative values of t are allowed; that is, if there is a random variable ...
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.