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The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution, Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution is the distribution of the x-intercept of a ray issuing from with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero.
In economics, the Gini coefficient, also known as the Gini index or Gini ratio, is a measure of statistical dispersion intended to represent the income inequality or the wealth inequality within a nation or a social group. The Gini coefficient was developed by the statistician and sociologist Corrado Gini.
In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. It is defined as the difference between the 75th and 25th percentiles of the data. To calculate the IQR, the data set is divided into quartiles, or four rank-ordered even parts via linear interpolation. These quartiles are denoted by Q1 (also called the lower quartile), Q2 (the median), and Q3 (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = Q3 − Q1.
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four.
In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way. There is one fewer quantile than the number of groups created. Common quantiles have special names, such as quartiles, deciles, and percentiles. The groups created are termed halves, thirds, quarters, etc., though sometimes the terms for the quantile are used for the groups created, rather than for the cut points.
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined.
In medicine and health-related fields, a reference range or reference interval is the range or the interval of values that is deemed normal for a physiological measurement in healthy persons. It is a basis for comparison for a physician or other health professional to interpret a set of test results for a particular patient. Some important reference ranges in medicine are reference ranges for blood tests and reference ranges for urine tests.
In statistics, rankits of a set of data are the expected values of the order statistics of a sample from the standard normal distribution the same size as the data. They are primarily used in the normal probability plot, a graphical technique for normality testing.
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In probability and statistics, the quantile function, associated with a probability distribution of a random variable, specifies the value of the random variable such that the probability of the variable being less than or equal to that value equals the given probability. Intuitively, the quantile function associates with a range at and below a probability input the likelihood that a random variable is realized in that range for some probability distribution. It is also called the percentile function, percent-point function or inverse cumulative distribution function.
Within computational biology, an MA plot is an application of a Bland–Altman plot for visual representation of genomic data. The plot visualizes the differences between measurements taken in two samples, by transforming the data onto M and A scales, then plotting these values. Though originally applied in the context of two channel DNA microarray gene expression data, MA plots are also used to visualise high-throughput sequencing analysis.
Quantile regression is a type of regression analysis used in statistics and econometrics. Whereas the method of least squares estimates the conditional mean of the response variable across values of the predictor variables, quantile regression estimates the conditional median of the response variable. Quantile regression is an extension of linear regression used when the conditions of linear regression are not met.
Academic grading in the United States commonly takes on the form of five, six or seven letter grades. Traditionally, the grades are A+, A, A−, B+, B, B−, C+, C, C−, D+, D, D− and F, with A+ being the highest and F being lowest. In some cases, grades can also be numerical. Numeric-to-letter-grade conversions generally vary from system to system and between disciplines and status.
In statistics, one purpose for the analysis of variance (ANOVA) is to analyze differences in means between groups. The test statistic, F, assumes independence of observations, homogeneous variances, and population normality. ANOVA on ranks is a statistic designed for situations when the normality assumption has been violated.
In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values. It is a measure of the skewness of a random variable's distribution—that is, the distribution's tendency to "lean" to one side or the other of the mean. Its calculation does not require any knowledge of the form of the underlying distribution—hence the name nonparametric. It has some desirable properties: it is zero for any symmetric distribution; it is unaffected by a scale shift; and it reveals either left- or right-skewness equally well. In some statistical samples it has been shown to be less powerful than the usual measures of skewness in detecting departures of the population from normality.
Response modeling methodology (RMM) is a general platform for statistical modeling of a linear/nonlinear relationship between a response variable and a linear predictor, often denoted the linear predictor function. It is generally assumed that the modeled relationship is monotone convex or monotone concave. However, many non-monotone functions, like the quadratic equation, are special cases of the general model.
References
- ↑ Amaratunga, D.; Cabrera, J. (2001). "Analysis of Data from Viral DNA Microchips". Journal of the American Statistical Association. 96 (456): 1161. doi:10.1198/016214501753381814. S2CID 18154109.
- ↑ Bolstad, B. M.; Irizarry, R. A.; Astrand, M.; Speed, T. P. (2003). "A comparison of normalization methods for high density oligonucleotide array data based on variance and bias". Bioinformatics. 19 (2): 185–193. doi: 10.1093/bioinformatics/19.2.185 . PMID 12538238.