/**
 * Useful matrix operations for multivariate samples.
 *
 * @since 1.0.0
 */
import * as RNEA from 'fp-ts/ReadonlyNonEmptyArray';
import * as V from './Vector';
import * as M from './Matrix';
/**
 * An observation is a (free) collection of data vectors, where N is the number of
 * variables associated with the observation
 *
 * @since 1.0.0
 * @category Model
 * @example
 *   // Given three subjects whose measurements are height, weight, shoe size, we can construct a correlation matrix as follows:
 *
 *   import * as V from '@jacob-alford/matrix-ts/Vector'
 *   import * as MStat from '@jacob-alford/matrix-ts/Multivariate'
 *
 *   const obs1 = V.fromTuple([167, 63, 8])
 *   const obs2 = V.fromTuple([200, 94, 12])
 *   const obs3 = V.fromTuple([160, 65, 9])
 *   const observations: MStat.MultivariateSample<3> = [obs1, obs2, obs3]
 *
 *   // This determines how mutually correlated the different variables are
 *   MStat.correlation(observations)
 */
export declare type MultivariateSample<N> = RNEA.ReadonlyNonEmptyArray<V.Vec<N, number>>;
/**
 * The average value over different variables
 *
 * @since 1.0.0
 * @category Multivariate Statistics
 */
export declare const mean: <N extends number>(s: MultivariateSample<N>) => V.Vec<N, number>;
/**
 * The difference in observation from a mean of MultivariateSample
 *
 * @since 1.0.0
 * @category Multivariate Statistics
 */
export declare const deviation: <N extends number>(s: MultivariateSample<N>) => MultivariateSample<N>;
/**
 * The covariance matrix where each index: i, j represent the variance between each random
 * variable of the Multivariatesample
 *
 * @since 1.0.0
 * @category Multivariate Statistics
 */
export declare const covariance: <N extends number>(s: MultivariateSample<N>) => M.Mat<N, N, number>;
/**
 * The correlation matrix where each index: i, j represent the correlation between those
 * two random variables
 *
 * @since 1.0.0
 * @category Multivariate Statistics
 */
export declare const correlation: <N extends number>(s: MultivariateSample<N>) => M.Mat<N, N, number>;
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