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PMF, PDF, CDF, Survival, and Quantile Functions

Install and import#

bash
npm install fintech-algorithms
ts
import { pmfPdfCdfSurvivalAndQuantileFunctions } from "fintech-algorithms/foundations/probability-distributions-and-simulation-basics/pmf-pdf-cdf-survival-and-quantile-functions";

Signature#

pmfPdfCdfSurvivalAndQuantileFunctions(input)

Reads an empirical sample from input.values and reports where the threshold input.x sits inside it, plus the sample quantile at probability input.p.

Parameters#

NameTypeNotes
inputD00InputOne record. values is the observed sample, x is the threshold to evaluate the empirical CDF and survival at, and p is the quantile probability. Other keys in the record are ignored.
values: non-empty list of finite numbers · p: between 0 and 1 inclusive

Returns#

D00Output

An object with cdf (share of values at or below x), survival (share strictly above x) and quantile (the linearly interpolated sample quantile at p).

Errors#

  • When p is missing or outside 0 to 1 — this check runs for every topic in the family — throws RangeError
  • When values is missing, empty, or contains a non-finite number — throws RangeError

Complexity: time O(n log n), space O(n).

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#

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#

pmfPdfCdfSurvivalAndQuantileFunctions(input)

Returns#

object with 2 fields: cdf, survival

{
  "cdf": 0.8,
  "survival": 0.2
}

Diagrams#

PMF, PDF, CDF, Survival, and Quantile Functions — article hero
PMF, PDF, CDF, Survival, and Quantile Functions — calculation ledger
PMF, PDF, CDF, Survival, and Quantile Functions — concept anatomy
PMF, PDF, CDF, Survival, and Quantile Functions — failure boundary
PMF, PDF, CDF, Survival, and Quantile Functions — method map
PMF, PDF, CDF, Survival, and Quantile Functions — scenario contrast

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#

The rest of the Probability Distributions and Simulation Basics family#