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In statistics, a Q–Q plot (quantile–quantile plot) is a probability plot, a graphical method for comparing two probability distributions by plotting their quantiles against each other. [1] A point ( x , y ) on the plot corresponds to one of the quantiles of the second distribution ( y -coordinate) plotted against the same quantile of the ...
A graphical tool for assessing normality is the normal probability plot, a quantile-quantile plot (QQ plot) of the standardized data against the standard normal distribution. Here the correlation between the sample data and normal quantiles (a measure of the goodness of fit) measures how well the data are modeled by a normal distribution. For ...
Quantile functions are used in both statistical applications and Monte Carlo methods. The quantile function is one way of prescribing a probability distribution, and it is an alternative to the probability density function (pdf) or probability mass function, the cumulative distribution function (cdf) and the characteristic function.
For processes that produce homogeneous batches (e.g., chemical) where repeat measurements vary primarily because of measurement error; The "chart" actually consists of a pair of charts: one, the individuals chart, displays the individual measured values; the other, the moving range chart, displays the difference from one point to the next.
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 (or other quantiles) of the response variable.
The standard measure of a distribution's kurtosis, originating with Karl Pearson, [1] is a scaled version of the fourth moment of the distribution. This number is related to the tails of the distribution, not its peak; [ 2 ] hence, the sometimes-seen characterization of kurtosis as " peakedness " is incorrect.
The quantile function is the inverse of the cumulative distribution function if the cumulative distribution function is monotonically increasing because the one-to-one correspondence between the input and output of the cumulative distribution function holds.
In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. [1] 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.