Cumulative distribution function
A cumulative distribution function gives the probability that a random variable is less than or equal to each specified value.
Statistics Every Programmer Needs
A cumulative distribution function is a function that gives the probability that a random variable is less than or equal to a specified value.
- How it is used
- Uses cumulative probabilities to answer threshold and interval questions and map random numbers to Monte Carlo outcomes.
- How deep it goes
- Defines continuous and discrete CDFs, gives their properties, and works cumulative sums and intervals without formal proofs.
- Examples
- Calculates a two-dice threshold and tabulates cumulative probabilities for Poisson-modeled employee absences.
- What you can do after
- Apply it via SciPy’s norm.cdf() and poisson.cdf() to calculate probabilities and prepare cumulative values for simulation.
Read how Statistics Every Programmer Needs explains cumulative distribution function →
Grokking Statistics
A function that returns the probability that a random variable is less than or equal to a specified value.
- How it is used
- Calculates probabilities over value ranges in beta and normal distributions.
- How deep it goes
- Defines CDFs as left-tail areas and demonstrates interval subtraction, while delegating integration to SciPy.
- Examples
- Uses success rates from a beta distribution and golden retriever weights from a normal distribution.
- What you can do after
- Apply it via SciPy's `beta.cdf()` and `norm.cdf()` to calculate probabilities for bounded ranges.
Read how Grokking Statistics explains cumulative distribution function →
Bayesian Optimization in Action
A cumulative distribution function method returns the probability that a random variable is less than or equal to a specified value.
- How it is used
- Converts predictive distributions into probability-of-improvement scores for expensive black-box optimization.
- How deep it goes
- Defines the CDF geometrically and demonstrates its complement numerically, stopping short of deriving the normal CDF.
- Examples
- Uses predictive values at points 0 and 3, highlighted normal-curve areas, and a PyTorch CDF calculation returning 0.8305.
- What you can do after
- Apply it via PyTorch’s Normal.cdf() and subtract the result from 1 to score candidate improvement.
Read how Bayesian Optimization in Action explains cumulative distribution function →
Build a Robo-Advisor with Python (From Scratch)
A cumulative distribution function gives the probability that a random variable is less than or equal to a specified value.
- How it is used
- Computes wealth-state transition probabilities for dynamic programming in goals-based financial planning.
- How deep it goes
- Explains interval probabilities and implements adjacent CDF differences, while deferring alternative distribution implementations.
- Examples
- Uses wealth-state midpoints, zero and infinite boundary values, and a normal-return transition calculation.
- What you can do after
- Apply it via SciPy to convert modeled wealth distributions into transition probabilities.
Read how Build a Robo-Advisor with Python (From Scratch) explains cumulative distribution function →
Related concepts
- probability densityproduced by · A probability density function is a nonnegative function describing the distribution of a continuous random variable, whose integral over a region gives the probability of values in that region.
- inverse cumulative density functionequivalent to · An inverse cumulative distribution function maps a cumulative probability to the corresponding value of a random variable.
- probability distributionproduced by · A probability distribution is a mathematical specification assigning probabilities to the possible values or outcomes of a random variable, with total probability one.
- scipy.stats.norm.cdfused by · scipy.stats.norm.cdf is a SciPy function that evaluates the cumulative distribution function of a normal distribution at specified values.
- step functionuses · A step function is a piecewise-constant function that changes abruptly between discrete output values when its input crosses one or more specified thresholds.
These guides are generated from the text of Manning books by Manning's knowledge graph and link to the sections they draw on. The full books are available on liveBook and at manning.com.