Search results
Results from the WOW.Com Content Network
Statistical assumptions can be put into two classes, depending upon which approach to inference is used. Model-based assumptions. These include the following three types: Distributional assumptions. Where a statistical model involves terms relating to random errors, assumptions may be made about the probability distribution of these errors. [5]
The assumption of a particular form for the relation between Y and X is another source of uncertainty. A properly conducted regression analysis will include an assessment of how well the assumed form is matched by the observed data, but it can only do so within the range of values of the independent variables actually available.
The general ARMA model was described in the 1951 thesis of Peter Whittle, who used mathematical analysis (Laurent series and Fourier analysis) and statistical inference. [ 12 ] [ 13 ] ARMA models were popularized by a 1970 book by George E. P. Box and Jenkins, who expounded an iterative ( Box–Jenkins ) method for choosing and estimating them.
Based on the assumption that the original data set is a realization of a random sample from a distribution of a specific parametric type, in this case a parametric model is fitted by parameter θ, often by maximum likelihood, and samples of random numbers are drawn from this fitted model. Usually the sample drawn has the same sample size as the ...
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process . [ 1 ]
Standard linear regression models with standard estimation techniques make a number of assumptions about the predictor variables, the response variable and their relationship. Numerous extensions have been developed that allow each of these assumptions to be relaxed (i.e. reduced to a weaker form), and in some cases eliminated entirely.
In time series analysis used in statistics and econometrics, autoregressive integrated moving average (ARIMA) and seasonal ARIMA (SARIMA) models are generalizations of the autoregressive moving average (ARMA) model to non-stationary series and periodic variation, respectively.
The mathematics of the distribution resulted from the authors' desire to make the standard deviation equal to about 1/6 of the range. [ 2 ] [ 3 ] The PERT distribution is widely used in risk analysis [ 4 ] to represent the uncertainty of the value of some quantity where one is relying on subjective estimates, because the three parameters ...