134 lines
4.2 KiB
Plaintext
134 lines
4.2 KiB
Plaintext
|
|
{{alias}}( x, y[, ...args][, options] )
|
|
Performs a chi-square goodness-of-fit test.
|
|
|
|
A chi-square goodness-of-fit test is computed for the null hypothesis that
|
|
the values of `x` come from the discrete probability distribution specified
|
|
by `y`.
|
|
|
|
The second argument can either be expected frequencies, population
|
|
probabilities summing to one, or a discrete probability distribution name to
|
|
test against.
|
|
|
|
When providing a discrete probability distribution name, distribution
|
|
parameters *must* be supplied as additional arguments.
|
|
|
|
The function returns an object containing the test statistic, p-value, and
|
|
decision.
|
|
|
|
By default, the p-value is computed using a chi-square distribution with
|
|
`k-1` degrees of freedom, where `k` is the length of `x`.
|
|
|
|
If provided distribution arguments are estimated (e.g., via maximum
|
|
likelihood estimation), the degrees of freedom should be corrected. Set the
|
|
`ddof` option to use `k-1-n` degrees of freedom, where `n` is the degrees of
|
|
freedom adjustment.
|
|
|
|
The chi-square approximation may be incorrect if the observed or expected
|
|
frequencies in each category are too small. Common practice is to require
|
|
frequencies greater than five.
|
|
|
|
Instead of relying on chi-square approximation to calculate the p-value, one
|
|
can use Monte Carlo simulation. When the `simulate` option is `true`, the
|
|
simulation is performed by re-sampling from the discrete probability
|
|
distribution specified by `y`.
|
|
|
|
Parameters
|
|
----------
|
|
x: ndarray|Array<number>|TypedArray
|
|
Observation frequencies.
|
|
|
|
y: ndarray|Array<number>|TypedArray|string
|
|
Expected frequencies, population probabilities, or a discrete
|
|
probability distribution name.
|
|
|
|
args: ...number (optional)
|
|
Distribution parameters. Distribution parameters will be passed to a
|
|
probability mass function (PMF) as arguments.
|
|
|
|
options: Object (optional)
|
|
Options.
|
|
|
|
options.alpha: number (optional)
|
|
Significance level of the hypothesis test. Must be on the interval
|
|
[0,1]. Default: 0.05.
|
|
|
|
options.ddof: number (optional)
|
|
Delta degrees of freedom adjustment. Default: 0.
|
|
|
|
options.simulate: boolean (optional)
|
|
Boolean indicating whether to calculate p-values by Monte Carlo
|
|
simulation. The simulation is performed by re-sampling from the discrete
|
|
distribution specified by `y`. Default: false.
|
|
|
|
options.iterations: number (optional)
|
|
Number of Monte Carlo iterations. Default: 500.
|
|
|
|
Returns
|
|
-------
|
|
out: Object
|
|
Test results object.
|
|
|
|
out.alpha: number
|
|
Significance level.
|
|
|
|
out.rejected: boolean
|
|
Test decision.
|
|
|
|
out.pValue: number
|
|
Test p-value.
|
|
|
|
out.statistic: number
|
|
Test statistic.
|
|
|
|
out.df: number|null
|
|
Degrees of freedom.
|
|
|
|
out.method: string
|
|
Test name.
|
|
|
|
out.toString: Function
|
|
Prints formatted output.
|
|
|
|
out.toJSON: Function
|
|
Serializes results as JSON.
|
|
|
|
Examples
|
|
--------
|
|
// Provide expected probabilities...
|
|
> var x = [ 89, 37, 30, 28, 2 ];
|
|
> var p = [ 0.40, 0.20, 0.20, 0.15, 0.05 ];
|
|
> var out = {{alias}}( x, p );
|
|
> var o = out.toJSON()
|
|
{ 'pValue': ~0.0406, 'statistic': ~9.9901, ... }
|
|
> out.toString()
|
|
|
|
// Set significance level...
|
|
> var opts = { 'alpha': 0.01 };
|
|
> out = {{alias}}( x, p, opts );
|
|
> out.toString()
|
|
|
|
// Calculate the test p-value via Monte Carlo simulation...
|
|
> x = [ 89, 37, 30, 28, 2 ];
|
|
> p = [ 0.40, 0.20, 0.20, 0.15, 0.05 ];
|
|
> opts = { 'simulate': true, 'iterations': 1000 };
|
|
> out = {{alias}}( x, p, opts );
|
|
> out.toString()
|
|
|
|
// Verify that data comes from Poisson distribution...
|
|
> var lambda = 3.0;
|
|
> var rpois = {{alias:@stdlib/random/base/poisson}}.factory( lambda );
|
|
> var len = 400;
|
|
> x = [];
|
|
> for ( var i = 0; i < len; i++ ) { x.push( rpois() ); };
|
|
|
|
// Generate a frequency table...
|
|
> var freqs = new {{alias:@stdlib/array/int32}}( len );
|
|
> for ( i = 0; i < len; i++ ) { freqs[ x[ i ] ] += 1; };
|
|
> out = {{alias}}( freqs, 'poisson', lambda );
|
|
> out.toString()
|
|
|
|
See Also
|
|
--------
|
|
|