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{{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
--------
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