What is the difference between PDF and CDF?

PDF (Probability Density Function) shows the relative likelihood of a value occurring, while CDF (Cumulative Distribution Function) shows the probability that the variable is less than or equal to a given value. The CDF is the integral of the PDF.

When should I use the Normal distribution vs Exponential distribution?

Use the Normal distribution for continuous data that is symmetric around the mean (e.g., heights, measurement errors). Use the Exponential distribution for modeling time between events in a Poisson process (e.g., time until equipment failure, customer arrivals).

What is a quantile (inverse CDF)?

A quantile is the value below which a given percentage of observations fall. For example, the 0.95 quantile (95th percentile) is the value where 95% of the distribution lies below it. The inverse CDF finds this value for any given probability.

How do I interpret the shaded regions in the PDF chart?

Shaded regions represent probability areas under the curve. For P(a < X < b), the shaded area between values a and b shows the probability that the random variable falls within that range. The total area under the entire PDF curve equals 1 (100% probability).

Free Probability Distribution Calculator with Charts

Distribution Setup

Choose distribution and set parameters

Mode

Distribution Family

Bell-shaped distribution, fundamental in statistics

Use cases: Measurement errors, Natural phenomena, Central limit theorem

Parameters

mean

Location parameter (center of distribution)

Scale parameter (standard deviation, must be > 0)

Quick Stats

Mean

0.0000

Std Dev

1.0000

Variance

1.0000

Median (p50)

0.0000

Results

Distribution Statistics

Central Tendency

Mean:0.0000

Spread

Variance:1.0000

Std Dev:1.0000

Shape

Skewness:0.0000

Kurtosis:0.0000

Entropy:1.4189

Quantiles

1th:-2.3263

5th:-1.6449

25th:-0.6745

50th:0.0000

75th:0.6745

95th:1.6449

99th:2.3263

Distribution Charts

PDF/PMF

CDF

Survival Function

Quantile Function

Interactive Distribution Charts

PDF/PMF

Relative likelihood of each value

CDF

Probability that X ≤ x

Survival

Probability that X > x

Quantile

Value x where P(X ≤ x) = p

Tip: Click on any chart to view it in full size with zoom controls. Use the Tools tab for probability calculations with visual highlights.

Probability Distributions

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Distribution Setup

Results

Distribution Statistics

Quantiles

Distribution Charts

Interactive Distribution Charts

Next steps

Notes & Assumptions

Learn More

Distribution Setup

Results

Distribution Statistics

Quantiles

Distribution Charts

Interactive Distribution Charts