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Index

PMP.PearsonType1 — Type
PearsonType1(a,b,α,β)

The Pearson Type 1 distribution with shape parameters α and β defined on the interval (a, b) has the probability density function for $a<y<b$

\[f(y; a, b, \alpha, \beta) = \frac{1}{B(\alpha, \beta)} \frac{(y-a)^{\alpha-1} (b-y)^{\beta-1}}{(b-a)^{\alpha+\beta-1}},\]

and 0 elsewhere.

PearsonType1()   # Pearson Type 1 distribution on the unit interval with shape parameters (1,1) i.e. Uniform(0, 1)


params(d)        # Get the parameters, i.e. (a, b, α, β)

location(d)      # Get the location parameter, i.e. a
scale(d)         # Get the scale parameter, i.e. b-a
shape(d)         # Get the shape parameters, i.e. (α, β)

External links

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PMP.PearsonType1b — Type
PearsonType1b(b,α,β)

The Pearson Type 1 distribution with shape parameters α and β defined on the interval (0, b) has the probability density function for $0<y<b$

\[f(y; b, \alpha, \beta) = \frac{1}{B(\alpha, \beta)} \frac{y^{\alpha-1} (b-y)^{\beta-1}}{b^{\alpha+\beta-1}},\]

and 0 elsewhere.

PearsonType1b()   # Pearson Type 1 distribution on the unit interval with shape parameters (1,1) i.e. Uniform(0, 1)


params(d)        # Get the parameters, i.e. (b, α, β)

scale(d)         # Get the scale parameter, i.e. b
shape(d)         # Get the shape parameters, i.e. (α, β)

External links

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PMP.PearsonType1c — Type
PearsonType1c(b,μ,ν)

The Pearson Type 1 distribution with shape parameters μ and ν defined on the interval (0, b) has the probability density function for $0<y<b$

\[f(y; b, \mu, \nu) = \frac{1}{B(\mu, \nu)} \frac{y^{\mu\nu-1} (b-y)^{\nu(1-\mu) - 1}}{b^{\nu-1}},\]

and 0 elsewhere.

PearsonType1c()   # Pearson Type 1 distribution on the unit interval with shape parameters (1/2,2) i.e. Uniform(0, 1)


params(d)        # Get the parameters, i.e. (b, μ, ν)

scale(d)         # Get the scale parameter, i.e. b
shape(d)         # Get the shape parameters, i.e. (μ, ν)
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Base.maximum — Method
maximum(pd::PearsonType1b)

Obtain the upper limit of the distribution pd, b.

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Base.maximum — Method
maximum(pd::PearsonType1)

Obtain the upper limit of the distribution pd, b.

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Base.minimum — Method
minimum(pd::PearsonType1b)

Obtain the lower limit of the distribution pd, 0.

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Base.minimum — Method
minimum(pd::PearsonType1)

Obtain the lower limit of the distribution pd, a.

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Base.rand — Method
rand(rng::Random.AbstractRNG, pd::PearsonType1b)

Generate a random realization of distribution pd.

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Base.rand — Method
rand(rng::Random.AbstractRNG, pd::PearsonType1)

Generate a random realization of the distribution pd.

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Distributions.cdf — Method
cdf(pd::PearsonType1, x::Real)

Compute the cumulative distribution function value of pd at point x.

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Distributions.cdf — Method
cdf(pd::PearsonType1b, x::Real)

Compute the cumulative distribution function value of pd at point x.

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Distributions.insupport — Method
insupport(pd::PearsonType1, x::Real)

Establish if the point x is within the support of the distribution pd.

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Distributions.insupport — Method
insupport(pd::PearsonType1b, x::Real)

Establish if the point x is within the support of the distribution pd.

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Distributions.logpdf — Method
logpdf(pd::PearsonType1, x::Real)

Compute the log of the value of the probability density function of pd at point x.

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Distributions.logpdf — Method
logpdf(pd::PearsonType1b, x::Real)

Compute the log of the value of the probability density function of pd at point x.

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Distributions.logpdf — Method
logpdf(pd::PearsonType1c, x::Real)

Compute the log of the value of the probability density function of pd at point x.

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PMP.PMP_GEV — Method
PMP_GEV(rain::Vector{<:Real}, date::Vector{DateTime}, return_time::Real, d₁::Int, d₂::Int)
PMP_GEV(rain::Vector{<:Real}, date::Vector{DateTime}, return_time::Real)

Estimation of the PMP by univariate GEV method, with a chosen return time.

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PMP.PMP_Hershfield — Method
PMP_Hershfield(rain_daily::Vector{<:Real}, date::Vector{DateTime}, K::Real, d₁::Int, d₂::Int)
PMP_Hershfield(rain_daily::Vector{<:Real}, date::Vector{DateTime}, K::Real)
PMP_Hershfield(rain_daily::Vector{<:Real}, date::Vector{DateTime}, d₁::Int, d₂::Int)
PMP_Hershfield(rain_daily::Vector{<:Real}, date::Vector{DateTime})

Estimation of the PMP by Hershfield empirical method.

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PMP.PMP_mm — Function
PMP_mm(rain_storm::Vector{<:Real}, pw_storm::Vector{<:Real}, date_storm::Vector{DateTime}, pw_max::Vector{<:Real})
PMP_mm(rain_storm::Vector{<:Real}, pw_storm::Vector{<:Real}, date_storm::Vector{Date}, pw_max::Vector{<:Real})

Estimation of the PMP by moisture maximization.

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PMP.PW_max — Function
PW_max(pw::Vector{<:Real}, date::Vector{DateTime})
PW_max(pw::Vector{<:Real}, date::Vector{Date})

Estimate the maximum precipitable water for each month of interest.

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PMP.PW_return_period — Function
PW_return_period(pw::Vector{<:Real}, date::Vector{DateTime}, return_period::Int=100)
PW_return_period(pw::Vector{<:Real}, date::Vector{Date}, return_period::Int=100)

Estimate the precipitable water return value for each month of interest for a given return period.

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PMP.PW_storm — Function
PW_storm(storm_date::Vector{DateTime}, dewpoint::Vector{<:Real}, dewpoint_date::Vector{DateTime}, d₂::Int, frequency::Int, time_int::Int=12)
PW_storm(storm_date::Vector{Date}, dewpoint::Vector{<:Real}, dewpoint_date::Vector{DateTime}, d₂::Int, frequency::Int, time_int::Int=12)
PW_storm(storm_date::Vector{DateTime}, dewpoint::Vector{<:Real}, dewpoint_date::Vector{Date}, d₂::Int, frequency::Int, time_int::Int=12)
PW_storm(storm_date::Vector{Date}, dewpoint::Vector{<:Real}, dewpoint_date::Vector{Date}, d₂::Int, frequency::Int, time_int::Int=12)

Get the precipitable water for each storm.

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PMP.dataset — Method
dataset(name::String)::DataFrame

Load the dataset associated with name.

Datasets available:

  • rain: observed precipitations (in mm) recorded at the Montréal-Trudeau International Airport;
  • dewpoint: observed dew point (in °C) recorded at the Montréal-Trudeau International Airport.

Examples

julia> PMP.dataset("rain")
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PMP.dewpoint_to_PW — Method
dewpoint_to_PW(dew_data::Real)

Convert dew point observation in precipitable water (PW).

The relation is given by the Table A.1.1 of the annex of the "Manual on Estimation of Probable Maximum Precipitation (PMP)" (WMO, 2009).

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PMP.get_max_persisting_dew — Function
get_max_persisting_dew(dewpoint::Vector{<:Real}, frequency::Int, time_int::Int=12)

Get the maximum persisting dewpoint of a storm for which data are taken at a given frequency.

The highest persisting dewpoint for some specified time interval is the value equalled or exceeded at all observations during the period (WMO, 2009).

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PMP.logcdf — Method
logcdf(pd::PearsonType1, x::Real)

Compute the log cumulative distribution function value of pd at point x.

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PMP.logcdf — Method
logcdf(pd::PearsonType1b, x::Real)

Compute the log cumulative distribution function value of pd at point x.

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PMP.storm_maximization — Function
storm_maximization(rain_storm::Vector{<:Real}, pw_storm::Vector{<:Real}, date_storm::Vector{DateTime}, pw_max::Vector{<:Real})
storm_maximization(rain_storm::Vector{<:Real}, pw_storm::Vector{<:Real}, date_storm::Vector{Date}, pw_max::Vector{<:Real})

Estimation of the maximization ratio, effective precipitation and maximized precipitation.

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PMP.storm_selection — Function
storm_selection(rain::Vector{<:Real}, date::Vector{DateTime}, p::Real, d₁::Int, d₂::Int=72)
storm_selection(rain::Vector{<:Real}, date::Vector{Date}, p::Real, d₁::Int, d₂::Int=72)
storm_selection(rain::Vector{<:Real}, date::Vector{DateTime}, p::Real)
storm_selection(rain::Vector{<:Real}, date::Vector{Date}, p::Real)

Select the PMP magnitude storms of each year.

The function choose the greatest precipitations of duration d₂ from data of duration d₁ while avoiding overlap. The function then select the p (a proportion) greatest storm of each year to be maximized.

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PMP.total_precipitation — Function
total_precipitation(rain::Vector{<:Real}, date::Vector{DateTime}, d₁::Int, d₂::Int)
total_precipitation(rain::Vector{<:Real}, date::Vector{Date}, d₁::Int, d₂::Int)

Estimate the greatest precipitations taken over a given duration d₁ on a longer duration d₂.

The function choose the greatest precipitations of duration d₂ while avoiding overlap. Datasets rain and date should not contain missing data.

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PMP.update_stepsize — Method
update_stepsize(δ::Real, accrate::Real)

Update of the random walk step size for the Metropolis-Hastings algorithm

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Statistics.std — Method
std(pd::PearsonType1b)

Obtain the standard deviation of the distribution pd.

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Statistics.std — Method
std(pd::PearsonType1)

Obtain the standard deviation of the distribution pd.

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StatsAPI.params — Method
shape(pd::PearsonType1)

Obtain all distribution parameters a, b, α and β.

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StatsBase.entropy — Method
entropy(pd::PearsonType1b)
entropy(pd::PearsonType1b, base::Real)

Compute the entropy value of distribution pd, w.r.t. a given base if given.

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StatsBase.entropy — Method
entropy(pd::PearsonType1)
entropy(pd::PearsonType1, base::Real)

Compute the entropy value of distribution pd, w.r.t. a given base if given.

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StatsBase.kurtosis — Method
kurtosis(pd::PearsonType1b)
kurtosis(pd::PearsonType1b, correction::Bool)

Obtain the excess kurtosis (if correction = false) or kurtosis (if correction = true) of the distribution pd .

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StatsBase.kurtosis — Method
kurtosis(pd::PearsonType1)
kurtosis(pd::PearsonType1, correction::Bool)

Obtain the excess kurtosis (if correction = false) or kurtosis (if correction = true) of the distribution pd .

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StatsBase.modes — Method
modes(pd::PearsonType1b)

Obtain all modes (if this makes sense) of the distribution pd.

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StatsBase.modes — Method
modes(pd::PearsonType1)

Obtain all modes (if this makes sense) of the distribution pd.

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