Functions

mrlplot(y::Vector{<:Real}, steps::Int = 100)

Mean residual plot

probplot(pd::Distribution, y::AbstractVector{<:Real})

Generate a probability–probability plot comparing the empirical distribution of y against the theoretical distribution pd.

Details

Arguments

• pd: A univariate probability distribution from Distributions.jl.
• y: A sample vector of real-valued observations.

Returns

A Gadfly.Plot object.

Example

using Distributions, ExtremePlots

y = rand(Gumbel(), 100)
p = probplot(Gumbel(), y)

qqplot(x::AbstractVector{<:Real}, y::AbstractVector{<:Real};
       interpolation::Bool=true, title::String="",
       xlabel::String="Empirical quantiles", ylabel::String="Empirical quantiles")

Create a quantile-quantile plot comparing two empirical distributions.

Details

Arguments

• x: Reference data vector, used to compute theoretical or sample quantiles.
• y: Observed data vector to be compared.
• interpolation: If true (default), quantiles are matched via interpolation based on ECDF. If false, the shortest length is sampled from both vectors without replacement and sorted.
• title: Title of the plot.
• xlabel: Label for the x-axis (default: "Empirical quantiles").
• ylabel: Label for the y-axis (default: "Empirical quantiles").

Returns

A Gadfly plot object.

qqplot(pd::Distribution, y::AbstractVector{<:Real})

Generate a quantile-quantile plot comparing the empirical qunatile of y against the theoretical quantiles of pd.

Details

Arguments

• pd: A univariate probability distribution from Distributions.jl.
• y: A sample vector of real-valued observations.

Returns

A Gadfly.Plot object.

Example

using Distributions, ExtremePlots

y = rand(Gumbel(), 100)
p = qqplot(Gumbel(), y)

returnlevelplot(pd::Distribution, y::AbstractVector{<:Real}; title::String="")

Generate a return level plot comparing empirical return levels with theoretical return levels from a fitted probability distribution.

Details

Arguments

• pd: A univariate distribution from Distributions.jl, representing the theoretical model.
• y: A vector of real-valued observations (e.g., annual maxima).
• title: (Optional) Title for the plot.

Returns

A Gadfly.Plot object showing:

• Points: Empirical return levels computed using the Gumbel plotting position.
• Dashed Line: Theoretical return levels computed from the quantile function of pd.

Example

using Gadfly, Distributions
y = rand(Gumbel(0, 1), 100)
returnlevelplot(Gumbel(0, 1), y, title="Return level plot")

diagnosticplots(fm::AbstractFittedExtremeValueModel)

Diagnostic plots

qqplotci(fm::AbstractFittedExtremeValueModel, α::Real = 0.05;
         title::String = "",
         xlabel::String = "Model quantile",
         ylabel::String = "Empirical quantile")

Generates a Quantile-Quantile (QQ) plot with pointwise confidence or credible intervals for a fitted extreme value model.

The plot compares the empirical quantiles to the model-predicted quantiles, and adds pointwise confidence intervals of level 1 - α.

Arguments

• fm: A fitted extreme value model (AbstractFittedExtremeValueModel)
• α: Significance level for the interval (default: 0.05)
• title: Plot title
• xlabel, ylabel: Axis labels

Returns

• A Gadfly.Plot object

Notes

• This function is currently only available for stationary models (i.e., with no covariates).

See also

• returnlevelplotci, qqplot

Example

```julia using Distributions, Extremes

pd = GeneralizedExtremeValue(0, 1, 0) y = rand(pd, 300) fm = gevfit(y)

qqplotci(fm)

returnlevelplotci(fm::AbstractFittedExtremeValueModel, α::Real = 0.05;
                  title::String = "",
                  xlabel::String = "Return period",
                  ylabel::String = "Return level")

Generates a return level plot with pointwise confidence or credible intervals for a fitted extreme value model.

Details

The return level plot displays the empirical and model-based return levels against return periods on a logarithmic x-axis, with confidence intervals of level 1 - α.

Arguments

• fm: A fitted extreme value model (AbstractFittedExtremeValueModel)
• α: Significance level for the confidence interval (default: 0.05)
• title: Title of the plot (optional)
• xlabel, ylabel: Axis labels (optional)

Returns

• A Gadfly.Plot object showing:
  • Empirical return levels (points)
  • Model-predicted return levels (dashed line)
  • Confidence or credible interval (shaded ribbon)

Notes

• This function is currently only available for stationary models (i.e., without covariates).
• Return periods are displayed on a base-10 logarithmic scale.

See also

• qqplotci, returnlevelplot

Example

```julia using Distributions, Extremes

pd = GeneralizedExtremeValue(0, 1, 0) y = rand(pd, 300) fm = gevfit(y)

returnlevelplotci(fm)