inst/help/LDchisq.md

In jasp-stats/jaspDistributions: Distributions Module for JASP

Chi-squared Distribution

Demonstration of the chi-squared distribution.

Show Distribution

Displays theoretical chi-squared distribution, given specified parameter values.

Parameters

• k: The shape parameter governs the shape of the density function.
• λ: The non-centrality parameter represents the hypothetical deviation in the sums of square differences.

Display

• Explanatory text: Displays explanatory text
• Parameters, support, and moments: Displays the definition of parameters, the support of the random variable, and the moments of the theoretical distribution
• Probability density function: Displays the probability density plot
• Cumulative distribution function: Displays the cumulative distribution plot
• Quantile function: Displays the quantile plot

Options

• Range of x from ... to ... : Defines the limits of the x-axis of the probability density plot and cumulative distribution plot, and the limits of the y-axis of the quantile plot.
• Highlight density: Highlights the probability density on the probability density plot and cumulative distribution plot at specified values of x
• Highlight probability: Highlights the probability in between the specified values of x in the density plot (area under the curve), and highlights the cumulative probability at the specified values in the cumulative distribution plot
• Interval: Select the bounds of the interval to display: Density is highlighted at the lower and upper bounds, the probability is displayed for the specified interval.

Generate and Display Data

• Variable name: Specify the name of the variable. Once filled, creates a column with samples drawn from the specified distribution in the current data set.
• Number of samples: Specify the number of samples.

• Draw samples: Sample from the theoretical distribution.

• Get variable from data set: Select a variable to display and fit with the theoretical distribution.

Statistics

• Descriptives: Displays a descriptive table of the selected variable.
• First ... moments: Displays a table with the raw and central sample moments of the selected variable. Defaults to first 2 moments.

Plots

• Histogram with ... bins: Display a histogram of the selected variable with the number of specified bins.
• Empirical cumulative distribution: Displays an empirical cumulative distribution plot of the selected variable.

Estimate Parameters

• Maximum likelihood: Estimates the parameters by the values in the domain at which the likelihood function is maximized. The likelihood function fixes the data argument (based on the selected variable) in the theoretical density function and views it as a function of the parameters. The optimization procedure is initialized with the values for the parameters entered under "Show Distribution".

Output

• Estimates: Displays a table with the parameter estimates. Changing parametrization changes which parameters are displayed.
  • Std. error: Displays the standard error of the parameter estimates
  • Confidence interval: Displays the confidence interval of the parameters at the specified confidence level.

Assess Fit

Plots

• Histogram vs. theoretical pdf: Displays a histogram of the selected variable overlayed with the probability density function of the fitted distribution
• Empirical vs. theoretical cdf: Displays an empirical cumulative distribution plot overlayed with the cumulative distribution function of the fitted distribution
• Q-Q plot: Displays the quantile-quantile plot. The x-axis shows the theoretical quantiles of the data points under the fitted distribution, the y-axis shows the empirical quantiles of the selected variable.
• P-P plot: Displays the probability-probability plot. The x-axis shows the theoretical value of the cumulative density function of the data points under the fitted distribution, the y-axis shows the empirical percentiles of the selected variable.

Statistics

• Kolmogorov-Smirnov: Displays the Kolmogorov-Smirnov test
• Cramér-von Mises: Displays the Cramér-von Mises test
• Anderson-Darling: Displays the Anderson-Darling test

jasp-stats/jaspDistributions documentation built on April 5, 2025, 3:46 p.m.