## Probability

Calculate probabilities and statistical distributions reliably.

Probability functions are fundamental for analyzing random events and statistical data. Calcul.io offers a variety of probability functions including distributions (normal, binomial, Poisson, etc.), cumulative distribution functions (CDFs), and probability density functions (PDFs). These functions are crucial for fields such as finance, insurance, and scientific research.

Our probability functions enable you to model uncertainties, calculate risks, and make informed decisions based on statistical evidence. Whether you are conducting experiments, performing data analysis, or simulating stochastic processes, Calcul.io provides the reliable tools you need for accurate probability computations.

combinations | Compute the number of combinations of n items taken k at a time |

combinationsWithRep | Compute the number of combinations of n items taken k at a time with replacements. |

factorial | Compute the factorial of a value |

gamma | Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation. |

kldivergence | Calculate the Kullback-Leibler (KL) divergence between two distributions. |

lgamma | Logarithm of the gamma function for real, positive numbers and complex numbers, using Lanczos approximation for numbers and Stirling series for complex numbers. |

multinomial | Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0. |

permutations | Compute the number of permutations of n items taken k at a time |

pickRandom | Pick a random entry from a given array. |

random | Return a random number. |

randomInt | Return a random integer number |