Generate Random Values
Overview
LabPlot can fill columns with random values drawn from various statistical distributions. This feature uses the GNU Scientific Library (GSL) random number generation functions and supports 36 different probability distributions including both continuous and discrete distributions.
Random values can be generated for numeric column types (Double, Integer, BigInt) and the distribution parameters are stored with the column, allowing regeneration with the same settings.
How to Generate Random Values
Select one or more columns in the spreadsheet
Right-click → Fill with Random Values (or from the menu)
Choose a distribution from the dropdown list
Configure the distribution parameters
Optionally set a seed for reproducible results
Click Generate
Note
If you specify a seed value, the same sequence of random numbers will be generated each time. This is useful for reproducible results. If no seed is specified, the current timestamp is used.
Available Distributions
Continuous Distributions
Gaussian (Normal)
The normal distribution with mean μ and standard deviation σ.
Parameters:
μ (mu) - Mean/location parameter
σ (sigma) - Standard deviation (scale parameter)
Use cases: Natural phenomena, measurement errors, central limit theorem applications
Example values:
Standard normal: μ = 0, σ = 1
Custom: μ = 100, σ = 15 (e.g., IQ scores)
Exponential
Models time between events in a Poisson process.
Parameters:
λ (lambda) - Rate parameter (1/mean)
μ (mu) - Location shift
Use cases: Waiting times, decay processes, reliability analysis
Laplace (Double Exponential)
Symmetric exponential distribution around the mean.
Parameters:
μ (mu) - Location parameter
σ (sigma) - Scale parameter
Use cases: Financial returns, signal processing, robust statistics
Cauchy (Lorentz)
Heavy-tailed distribution (no defined mean or variance).
Parameters:
γ (gamma) - Scale parameter
μ (mu) - Location parameter
Use cases: Resonance phenomena, statistical outliers
Rayleigh
Models magnitude of a 2D random vector with independent Gaussian components.
Parameters:
σ (sigma) - Scale parameter
Use cases: Wind speed, wave heights, communication systems
Gamma
Flexible continuous distribution for positive values.
Parameters:
k - Shape parameter (α)
θ (theta) - Scale parameter (β)
Use cases: Waiting times, rainfall amounts, insurance claims
Special cases:
k = 1: Exponential distribution
k = n/2, θ = 2: Chi-squared distribution with n degrees of freedom
Weibull
Models failure rates and lifetime analysis.
Parameters:
λ (lambda) - Scale parameter
k - Shape parameter
Use cases: Reliability engineering, survival analysis, wind speed modeling
Beta
Bounded distribution on [0, 1].
Parameters:
α (alpha) - First shape parameter
β (beta) - Second shape parameter
Use cases: Probabilities, proportions, Bayesian priors
Lognormal
Distribution of a variable whose logarithm is normally distributed.
Parameters:
μ (mu) - Mean of log(X)
σ (sigma) - Standard deviation of log(X)
Use cases: Income distributions, particle sizes, stock prices
Student’s t-distribution
Heavy-tailed distribution, reduces to normal as degrees of freedom increase.
Parameters:
ν (nu) - Degrees of freedom
Use cases: Small sample statistics, robust inference
Chi-squared
Distribution of sum of squared standard normal variables.
Parameters:
k - Degrees of freedom
Use cases: Goodness-of-fit tests, variance estimation
F-distribution
Ratio of two chi-squared distributions.
Parameters:
d₁ - Numerator degrees of freedom
d₂ - Denominator degrees of freedom
Use cases: ANOVA, regression analysis
Logistic
S-shaped distribution similar to normal but with heavier tails.
Parameters:
μ (mu) - Location parameter
s - Scale parameter
Use cases: Growth models, neural networks, classification
Pareto
Power-law distribution.
Parameters:
a - Shape parameter (tail index)
b - Scale parameter (minimum value)
Use cases: Income distribution, city sizes, network degrees
Gumbel (Type I and Type II)
Extreme value distributions.
Parameters:
μ (mu) - Location parameter
σ (sigma) - Scale parameter
Use cases: Maximum/minimum values, flood analysis, material strength
Flat (Uniform)
Constant probability over an interval.
Parameters:
a - Lower bound
b - Upper bound
Use cases: Random sampling, Monte Carlo simulations
Discrete Distributions
Poisson
Models count of events in fixed interval.
Parameters:
λ (lambda) - Average rate (mean = variance)
Use cases: Call arrivals, defect counts, rare events
Example values:
Low rate: λ = 2 (average 2 events)
High rate: λ = 20 (average 20 events)
Binomial
Number of successes in n independent trials.
Parameters:
p - Success probability (0 < p < 1)
n - Number of trials
Use cases: Quality control, surveys, coin flips
Example: n = 10, p = 0.3 (expect ~3 successes)
Bernoulli
Single trial with two outcomes (special case of binomial with n=1).
Parameters:
p - Success probability
Use cases: Yes/no decisions, pass/fail tests
Geometric
Number of trials until first success.
Parameters:
p - Success probability per trial
Use cases: Waiting time for first event
Negative Binomial (Pascal)
Number of failures before r successes.
Parameters:
p - Success probability
r - Number of successes to wait for
Use cases: Overdispersed count data
Hypergeometric
Sampling without replacement.
Parameters:
N - Population size
K - Number of success states in population
n - Number of draws
Use cases: Quality control sampling, card games
Logarithmic
Logarithmic series distribution.
Parameters:
p - Parameter (0 < p < 1)
Use cases: Species abundance, network analysis
Specialized Distributions
Landau
Describes energy loss of charged particles passing through matter.
Parameters: None (parameter-free)
Use cases: Particle physics
Lévy Alpha-Stable
Generalized central limit theorem distributions.
Parameters:
c - Scale parameter
α (alpha) - Stability parameter (0 < α ≤ 2)
Use cases: Financial modeling, complex systems
Lévy Skew Alpha-Stable
Asymmetric version of Lévy stable distributions.
Parameters:
c - Scale parameter
α (alpha) - Stability parameter
β (beta) - Skewness parameter (-1 ≤ β ≤ 1)
Gaussian Tail
Truncated Gaussian distribution (only values beyond a threshold).
Parameters:
μ (mu) - Mean
σ (sigma) - Standard deviation
a - Lower threshold (tail starts at)
Use cases: Extreme value analysis, truncated data
Rayleigh Tail
Truncated Rayleigh distribution.
Parameters:
μ (mu) - Location shift
σ (sigma) - Scale
a - Lower threshold
Exponential Power
Generalization of Gaussian and Laplace distributions.
Parameters:
μ (mu) - Location
σ (sigma) - Scale
b - Shape (b=2: Gaussian, b=1: Laplace)
Maxwell-Boltzmann
Speed distribution of particles in ideal gas.
Parameters:
a - Temperature-related scale parameter
Use cases: Statistical mechanics, molecular dynamics
Triangular
Simple distribution with linear increase and decrease.
Parameters:
a - Lower limit
b - Upper limit
c - Mode (peak location)
Use cases: Rough approximations, risk analysis when little data available
Sech (Hyperbolic Secant)
Symmetric distribution with specific tail behavior.
Parameters: Scale and location parameters
Lévy
Special case of Lévy alpha-stable (α = 0.5).
Parameters:
c - Scale parameter
μ (mu) - Location
Fréchet
Type II extreme value distribution.
Parameters:
α (alpha) - Shape
s - Scale
m - Location
Tips and Best Practices
Choosing a Distribution
Gaussian/Normal: Default choice for continuous data with symmetric bell shape
Uniform: When all values in a range are equally likely
Exponential: For waiting times or intervals between events
Poisson: For count data (number of events)
Binomial: For success/failure trials with fixed probability
Seed Values
Reproducible results: Use a fixed seed (e.g., 12345)
Different sequences: Change the seed value
Random sequences: Leave seed empty (uses current timestamp)
Parameter Selection
Check the distribution formula and parameter meanings
Start with standard parameter values (e.g., μ=0, σ=1 for Gaussian)
Adjust parameters to match your data characteristics
Use preview/statistics to verify the generated distribution
Common Patterns
Simulating measurement errors:
Distribution: Gaussian
μ = 0 (centered)
σ = 0.1 (small errors)
Generating test data in a range:
Distribution: Flat (Uniform)
a = 0 (minimum)
b = 100 (maximum)
Simulating arrival times:
Distribution: Poisson
λ = 5 (average 5 arrivals per time unit)
Adding realistic noise:
Distribution: Laplace
μ = 0
σ = 1 (heavier tails than Gaussian)
Column Mode Compatibility
Double columns: Accept all distributions with full precision
Integer columns: Values are rounded to nearest integer
BigInt columns: Values are rounded to nearest integer (wider range)
Text/DateTime columns: Cannot be filled with random values
Multiple Columns
When multiple columns are selected, each column receives independent random values from the same distribution. The values are not correlated unless you generate them in one column and copy/transform for others.
Regeneration
The distribution parameters are stored with the column. You can regenerate with the same settings by:
Select the column
Right-click → Fill with Random Values
The dialog shows the previous distribution and parameters
Click Generate to create a new sequence
Additional Resources
Distribution formulas and properties are shown in the dialog
For reproducible research, always document the seed value used