This article shows how to compute a confidence band for a Q-Q plot in SAS. A previous article shows how to construct confidence bands for the CDF of continuous univariate data. The bands can be added to a plot of the empirical CDF (ECDF) for the data. One of the
A previous article shows how to construct an empirical cumulative distribution function (ECDF) for univariate data by using PROC UNIVARIATE or in the SAS IML language. The ECDF is a tool for visualizing the distribution of a sample and is helpful for estimating quantiles in the data. In statistics, we
A previous article shows how to construct an empirical cumulative distribution function (ECDF) in SAS. The most common way is by using PROC UNIVARIATE, but you can also call the ECDF function in the SAS IML language. The ECDF is a tool for visualizing the distribution of a univariate sample
The empirical cumulative distribution function (ECDF) is an important tool in statistics. It is one of several plots you can use to visualize the shape of a data distribution. It is not used as often as the histogram, the kernel density estimate, and the box plot, but it is essential
This is the last article in a series about computing probabilities for the multivariate normal distribution. A previous article shows how to compute the probability of a standardized multivariate normal (MVN) distribution in an orthant for dimensions k=1, 2, and 3 by using the Childs-Sun formulas. The formulas are exact
In general, it is very difficult to compute a probability for a multivariate continuous distribution. For all continuous distributions, the probability requires solving a complicated multiple integral. For example, the probability for a bivariate normal distribution requires integrating the bivariate normal density over a two-dimensional (2-D) area. The probability for
A course in elementary statistics always introduces the "Z-score." A Z-score is the result of standardizing a normally distributed random variable. By subtracting the distribution's mean and dividing by its standard deviation, you transform a general normal random variable into a standardized variable that has zero mean and unit standard
A previous article discusses regression splines and how to use the EFFECT statement in SAS regression procedures to specify the location of knots for a regressor variable, X. Knots are breakpoints that partition the range of X into subintervals. The splines are defined on a set of adjacent subintervals. The
Splines are useful tools for fitting regression models to data. A spline replaces a single variable (call it X) with several other variables, which are a spline basis for X. When using a spline basis, the shape and location of the basis functions depend on the placement of knots. Knots
Did you know that, for skewed distributions, the sample median is a biased estimator of the population median? You can show this in two ways. For any distribution, you can run a Monte Carlo simulation that reveals the bias. And, for some distributions (such as the exponential distribution), you can
