/**
 * Computes the probability density function (PDF) of a normal distribution.
 *
 * Returns the PDF of the normal distribution with mean `mu` and standard deviation `sigma`, evaluated at `x`.
 * If `mu` and `sigma` are not provided, it defaults to the standard normal distribution (mu = 0, sigma = 1).
 *
 * @param x The value at which to evaluate the PDF
 * @param mu The mean of the normal distribution (defaults to 0)
 * @param sigma The standard deviation of the normal distribution (defaults to 1)
 * @returns The probability density function value at x
 * @throws If sigma is not a positive number
 *
 * @example Compute the standard normal PDF at x = 1
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(normpdf(1), 0.24197072451914337);
 *
 * ```
 *
 * @example Compute normal PDF with custom mean and standard deviation
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(normpdf(0, 10, 2), 7.433597573671488e-7);
 *
 * ```
 *
 * @example Compute normal PDF at the mean (should be maximum)
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(normpdf(5, 5, 1), 0.3989422804014327);
 *
 * ```
 *
 * @example Compute normal PDF for a large value (should be small)
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(normpdf(100, 50, 10), 1.486719514734298e-7);
 *
 * ```
 *
 * @example Compute normal PDF for a negative value
 * ```ts
 * import { assertEquals } from "jsr:@std/assert";
 *
 * assertEquals(normpdf(-1, 0, 1), 0.24197072451914337);
 * ```
 */
export default function normpdf(x: number, mu?: number, sigma?: number): number;
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