Statistics How To

Probability Distributions > Standard Power Distribution The standard power distribution has the probability density function f(x) = ΒxΒ-1; 0 < x < 1. The distribution has one shape parameter, Β. The distribution isn’t found very often in the literature, possibly because it isn’t a realistic model for real-world applications. One application is in random number … Read more

Probability Distributions > The sine distribution (also called Gilbert’s sine distribution) is a continuous probability distribution based on a part of the sine curve. It can fit a set of data that has several peaks, assuming that the data came from a genuine multimodal distribution and not a mixture distribution [1]. The distribution was introduced … Read more

Statistics Definitions > What is a Randomized Experiment? A randomized experiment involves randomly splitting a group into smaller groups: one group (the treatment group) receives the intervention, and one does not (the control group). The researcher selects the assignment mechanism, which is also random. Care is taken to choose a sampling method that results in … Read more

Statistics Definitions > The sample range is a popular and simple way to compare variability between different distributions of data. It is based on two values in a data set: the maximum, and the minimum: The sample range is an important measure of variability for continuous variables. It acts as an estimator for the range … Read more

Statistics Definitions > The sample median is the “middle” of a set of ordered sample data. For example, let’s say you had a sample of 5 data points: 1, 2, 4, 7, and 9. The sample median is the center number: How to Find the Sample Median In general, place the numbers in order from … Read more

< Probability Distributions < Power function distribution The power function distribution (PFD) is a flexible model used to analyze income distribution data, lifetime data, and failure processes. One of its key strengths is its mathematical simplicity, especially when compared to more complex distributions like the Weibull distribution. The PFD is a special case of the beta … Read more

Probability Distributions > The location-scale family of distributions includes many popular distributions like the normal distribution and uniform distribution. A random variable belongs to the location-scale family if its cumulative distribution FX (x | a, b):= Pr(X ≤ | a, b) is a function only of (x – a)/b [1]: Where: F(·) is a distribution … Read more

Probability Distributions > The term “special distribution” doesn’t refer to a specific distribution or family of distributions, but rather any probability distribution that is given a special name. These distributions are important in statistics for many reasons: they may model a wide range of phenomena, or they may be related to other special distributions via … Read more

Graphs and Charts > An attribute control chart is a way to track the production of defective items. The chart doesn’t tell you why the defects happened, but it does give you the total or average counts per unit. An attribute is a count or discrete data like conforming/non-conforming, pass/fail or yes/no. Attributes are qualitative, … Read more

Charts and Graphs > A U Chart is a type of attribute control chart used to control the mean number of defects in samples of differing sizes taken from a process. It is used when: Product characteristics can be evaluated with a discrete response: good/bad, pass/fail, or yes/no. You have more than 25 samples (ideally … Read more