GregoryLoredo

lcshape

Fields

• μlc: Vector of rate mean value for each bin
• σlc: Vector of standard deviation for the rate for each bin

orsum

Fields

• prob: Vector of probabilities for each possible bin number m
• maxm: Bin number showing the maximum probability

persum

Fields

• maxpow: Maximum power in the periodogram
• maxfreq: Frequency at the maximum power
• maxper: Period at the maximum power

BinMult(nbins::Vector{Int})

Arguments

• nbins is a vector with the number of events for each bin.

Compute the basic factor for the multiplicity of the binned events (Eq. 1.4 in Gregory & Lorendo (1992)).

BinningFactor(ω::Float64,Φ::Float64,m::Int,tlist::Vector{Float64})::BigFloat

Arguments

• ω is the angular frequency.
• Φ is the phase.
• m is the number of bins.
• tlist is the vector of arrival times.

Compute the binning factor (Eq. B4 in Gregory & Lorendo (1992)).

ComputeBinValues(m::Int,ω::Float64,Φ::Float64,tlist::Vector{Float64})

Arguments

• m is the number of bins.
• ω is the angular frequency.
• Φ is the phase.
• tlist is the vector of arrival times.

Compute the number of events falling in each bin of a model with m bins with given frequency and phase.

FrequencyRange(Tlist::Vector{Float64};tstart=minimum(Tlist),tend=maximum(Tlist),logspacing=false))

Arguments

• Tlist is the vector of arrival times.
• tstart is the minimum possible arrival time (default to the minimum of Tlist)
• tend is the minimum possible arrival time (default to the maximum of Tlist)
• logspacing generates a log-spaced frquency range.

Compute the frequency range to be analysed accordiong to the advises in Gregory & Lorendo (1992)).

FullBinMult(nbins::Vector{Int})

Arguments

• nbins is a vector with the number of events for each bin.

Compute the full multiplicity of the binned events (Eq. 1.4 in Gregory & Lorendo (1992)).

FullBinMultLog(nbins::Vector{Int})

Arguments

• nbins is a vector with the number of events for each bin.

Compute the full multiplicity of the binned events (Eq. 1.4 in Gregory & Lorendo (1992)).

The computation is here carried out by the logarithm.

LightCurveShape(ωr::Vector{Float64},m::Int,tlist::Vector{Float64};unc=false,progress=false,phasesteps=10)::lcshape

Arguments

• ωr is the vector of the analyzed frequencies.
• m is the number of bins.
• tlist is the vector of arrival times.
• unc computes light-curve uncertainty if selected.
• progress shows progress bars if selected.

Compute the light curve shape given the number m of bins and the input arrival time tlist (Eq. 7.10 in Gregory & Lorendo (1992)).

LightCurveSimpleShape(ω::Float64,Φ::Float64,m::Int,tlist::Vector{Float64};unc=false)::lcshape

Arguments

• ω is the angular frequency.
• Φ is the phase.
• m is the number of bins.
• tlist is the vector of arrival times.
• unc computes light-curve uncertainty if selected.

Compute the light curve shape given the angular frequency ω, the phase Φ, m bins given the input arrival time tlist (Eq. 4.3 in Gregory & Lorendo (1992)).

MarginalizedPeriodogram(Tlist::Vector{Float64},ωr::Vector{Float64};progress=false,phasesteps=10)

Arguments

• Tlist is the vector of arrival times.
• ωr is the vector of the analyzed frequencies.
• mmax is the maximum number of bins.
• progress shows progress bars if selected.

Compute the periodogram following Section 6 in Gregory & Lorendo (1992)).

OddRatioSummary(or::Vector{Real})::orsum

Arguments

• od is the vector of computed odd ratios for each considered light-curve bin number.

Compute the probability for a non constant model Eq. 5.2. in Gregory & Lorendo (1992)) and the bin number yileding the highest odd-ratio.

OddRatios(Tlist::Vector{Float64},ωr::Vector{Float64},mmax::Int;progress=false,phasesteps=10)

Arguments

• Tlist is the vector of arrival times.
• ωr is the vector of the analyzed frequencies.
• mmax is the maximum number of bins.
• progress shows progress bars if selected.

Compute the odd ratio following Appendix A in Gregory & Lorendo (1992)).

Periodogram(Tlist::Vector{Float64},ωr::Vector{Float64},m::Int,phasesteps=10)

Arguments

• Tlist is the vector of arrival times.
• ωr is the vector of the analyzed frequencies.
• m is the number of bins.

Compute the periodogram following Section 6 in Gregory & Lorendo (1992)).

PeriodogramSummary(per::Vector{BigFloat},ωr::Vector{Float64})::persum

Arguments

• per is the vector of powers for each considered frequency.
• ωr is the vector of the analyzed frequencies.

Plot the Odd Ratio as a function of the number of bins.

PlotLightCurve(lpl::lcshape;xlabel="",ylabel="",sigma=1.)

Arguments

• lpl is a light-curve shape structure.
• xlabel is the (optional) label for the x-axis.
• ylabel is the (optional) label for the y-axis.
• sigma is the number od standard deviation to be plotted.

Plot the light-curve in the given bins of the analysis.

PlotOddRatios(or::Vector{Real};xlabel="",ylabel="";xlabel="",ylabel="")

Arguments

• od is the vector of computed odd ratios for each considered light-curve bin number.
• xlabel is the (optional) label for the x-axis.
• ylabel is the (optional) label for the y-axis.

Plot the oddratio for each possible bin number.

PlotPeriodogram(per::Vector{BigFloat},ωr::Vector{Float64};xlabel="",ylabel="",pmax=2π/minimum(ωr),pmin=2π/maximum(ωr))

Arguments

• per is the vector of powers for each considered frequency.
• ωr is the vector of the analyzed frequencies.
• xlabel is the (optional) label for the x-axis.
• ylabel is the (optional) label for the y-axis.
• pmin is the minimum of the plotted periods (default minimum of the input data).
• pmax is the maximum of the plotted periods (default maximum of the input data).

Plot the periodogram as a function of the analysed frequencies.

WeightingFactor(njbin::Vector{Int},m::Int,totcnt::Int)::Vector{BigFloat}

Arguments

• njbin is the vector with the number of events in each model bin.
• m is the number of bins for the adopted model.
• totcnt is the total number of events in the analyzed dataset.

Compute the weighting factors for each bin of the model.

jt(m::Int,ω::Float64,Φ::Float64,t::Float64)

Arguments

• m is the number of bins.
• ω is the angular frequency.
• Φ is the phase.
• t is the time.

Compute the bin number at time tfor a model with m bins with given frequency and phase.

logStirlingApprox(n::Int)

Arguments

• n is the integer we want to use to compute the factorial.