Estimating a parametric lifetime distribution from superimposed
... Maintenance data provides information about the reliability of systems and components. For reparable systems, a failed component will be replaced with a new one, which, in some cases, can be assumed to have the same lifetime distribution as the old component. Estimation of the lifetime distribution ...
... Maintenance data provides information about the reliability of systems and components. For reparable systems, a failed component will be replaced with a new one, which, in some cases, can be assumed to have the same lifetime distribution as the old component. Estimation of the lifetime distribution ...
chapter 2 conditional probability and independence
... put into operation and after one it iscstill working. The question then is “What (Ayear ∪ B) is the probability that the device will continue working for another n months.” These are known as conditional probabilities because they are probabilities that are conditioned on the event that n ≥ 12. With ...
... put into operation and after one it iscstill working. The question then is “What (Ayear ∪ B) is the probability that the device will continue working for another n months.” These are known as conditional probabilities because they are probabilities that are conditioned on the event that n ≥ 12. With ...
Alg II CC-13 TE Probability of Compound Events
... dependent on the other event occurring. Have students look at compound probability problems by first determining whether the first event affects the second event. Once students determine whether the events are dependent or independent, they can select the appropriate equation. It may sometimes be di ...
... dependent on the other event occurring. Have students look at compound probability problems by first determining whether the first event affects the second event. Once students determine whether the events are dependent or independent, they can select the appropriate equation. It may sometimes be di ...
Reasoning System
... retract any existing assertions or axioms. ‡ Most formal logics have a monotonic consequence relation, meaning that adding a formula to a theory never produces a reduction of its set of consequences. In other words, a logic is monotonic if the truth of a proposition does not change when new informat ...
... retract any existing assertions or axioms. ‡ Most formal logics have a monotonic consequence relation, meaning that adding a formula to a theory never produces a reduction of its set of consequences. In other words, a logic is monotonic if the truth of a proposition does not change when new informat ...
June 11
... Link Additional Objects with work relating to a question to those questions (a chain link appears by the relevant question number) – see scoris assessor Quick Reference Guide page 19-20 for instructions as to how to do this – this guide is on the Cambridge Assessment Support Portal and new users may ...
... Link Additional Objects with work relating to a question to those questions (a chain link appears by the relevant question number) – see scoris assessor Quick Reference Guide page 19-20 for instructions as to how to do this – this guide is on the Cambridge Assessment Support Portal and new users may ...
Z - Earth Surface Hydrology
... plotted are the differences between the data and the model results. We can observe two features. First, the model time series seems to vary more smoothly then the observations. Secondly, there are noisy differences between model results and observations. These differences, which are called residuals ...
... plotted are the differences between the data and the model results. We can observe two features. First, the model time series seems to vary more smoothly then the observations. Secondly, there are noisy differences between model results and observations. These differences, which are called residuals ...
Chapter 1 Probability, Random Variables and
... from the door initially chosen to the one remaining door. For example, suppose the contestant choose door 1 initially, and that the host revealed that the large prize is not behind door 3. The contestant then has the chance to choose door 2 or to stay with door 1. In this example, B is the event whe ...
... from the door initially chosen to the one remaining door. For example, suppose the contestant choose door 1 initially, and that the host revealed that the large prize is not behind door 3. The contestant then has the chance to choose door 2 or to stay with door 1. In this example, B is the event whe ...
Power laws, Pareto distributions, and Zip`s law
... power-law behaviour, give empirical evidence for power laws in a variety of systems and describe some of the mechanisms by which power-law behaviour can arise. Readers interested in pursuing the subject further may also wish to consult the reviews by Sornette [18] and Mitzenmacher [19], as well as t ...
... power-law behaviour, give empirical evidence for power laws in a variety of systems and describe some of the mechanisms by which power-law behaviour can arise. Readers interested in pursuing the subject further may also wish to consult the reviews by Sornette [18] and Mitzenmacher [19], as well as t ...
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.