Lognormal Distribution and Positive Quantities

Install and import#

npm install fintech-algorithms

import { lognormalDistributionAndPositiveQuantities } from "fintech-algorithms/foundations/probability-distributions-and-simulation-basics/lognormal-distribution-and-positive-quantities";

Signature#

lognormalDistributionAndPositiveQuantities(input)

Evaluates the lognormal density and cumulative probability at input.x for a variable whose logarithm is normal with mean mu and standard deviation sigma, and returns the distribution's median.

Parameters#

Returns#

D00Output

An object with pdf, cdf and median. The median is always exp(mu). For x at or below zero the function returns pdf and cdf of zero rather than throwing, since the lognormal puts no mass there.

Errors#

• When p is missing or outside 0 to 1 — this check runs for every topic in the family — throws RangeError
• When sigma is zero or negative — this check runs for every topic from A05 onward — throws RangeError

Complexity: time O(1), space O(1).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

{
  "values": [0.2, 0.5, 0.7, 1, 1.4],
  "x": 1,
  "p": 0.3,
  "n": 5,
  "k": 2,
  "lambda": 2,
  "seed": 42,
  "sampleCount": 8,
  "mu": 0,
  "sigma": 1,
  "df": 5,
  "shape": 2,
  "scale": 1.5,
  "components": [
    {
      "weight": 0.7,
      "mean": 0,
      "sd": 1
    },
    {
      "weight": 0.3,
      "mean": 3,
      "sd": 0.8
    }
  ]
}

Call#

lognormalDistributionAndPositiveQuantities(input)

Returns#

object with 2 fields: pdf, cdf

{
  "pdf": 0.3989422804014327,
  "cdf": 0.5
}

Diagrams#

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

• Probability Distributions — NIST/SEMATECH e-Handbook
• Probability Distributions — SciPy User Guide
• Random Sampling — NumPy Documentation
• Historical-example decision

The rest of the Probability Distributions and Simulation Basics family#

• PMF, PDF, CDF, Survival, and Quantile FunctionsReads an empirical sample from input.values and reports where the threshold input.x sits inside it, plus the sample quantil…
• Bernoulli and Binomial DistributionsComputes the Bernoulli mean and the binomial probability mass and cumulative probability for k successes in n independent t…
• Poisson Distribution and Event CountsEvaluates the Poisson probability of exactly k events, the cumulative probability of at most k, and the distribution's mean…
• Uniform Distribution and Random SamplingDraws sampleCount values on the unit interval from a seeded linear congruential generator and reports the draws with their su…
• Normal Distribution and Standard NormalEvaluates the normal density and cumulative probability at input.x for a distribution with mean mu and standard deviation `…
• Student-t Distribution and Heavy TailsEvaluates the Student t density at input.x for df degrees of freedom and reports the distribution's variance, which only ex…
• Exponential, Gamma, and Weibull Waiting-Time ModelsEvaluates three waiting-time models at the same point input.x: the exponential survival function, the gamma density, and the …
• Mixture Distributions, Multimodality, and Fat TailsEvaluates a weighted mixture of normal components at input.x, which is how a single series can show more than one mode and fa…
• Random Sampling and Monte Carlo IntuitionEstimates the probability p by counting how many of sampleCount seeded uniform draws land at or below it, and reports how f…