/*

Statistical Dsitributions using Tendency

*/

// create a tendency object giving fixed upper and lower bounds
a = Tendency.new(1.0, 0.0);

// Linear Distributions:

// uniform
z = 500.collect({arg i; a.at(i)})
z.plot(discrete: true)

// lowpass
z = 500.collect({arg i; a.at(i, \lpRand)})
z.plot(discrete: true)

// highpass
z = 500.collect({arg i; a.at(i, \hpRand)})
z.plot(discrete: true)

// mean (bandpass)
z = 500.collect({arg i; a.at(i, \meanRand)})
z.plot(discrete: true)

// Non-linear distributions

// exponential
// we need to redefine the range to avoid 0.0

a = Tendency.new(1.0, 0.0001);
z = 500.collect({arg i; a.at(i, \expRand)})
z.plot(discrete: true)

// exponential with 'high' parameter control on density 
a = Tendency.new(0.5);
z = 500.collect({arg i; a.at(i, \exponential)})
z.plot(discrete: true, minval: 0, maxval: 5)

a = Tendency.new(1);
z = 500.collect({arg i; a.at(i, \exponential)})
z.plot(discrete: true, minval: 0, maxval: 5)

a = Tendency.new(2);
z = 500.collect({arg i; a.at(i, \exponential)})
z.plot(discrete: true, minval: 0, maxval: 5)

// gamma
// 'high' value controls mode or peak
a = Tendency.new(2.0);
z = 500.collect({arg i; a.at(i, \gamma)})
z.plot(discrete: true, minval: 0, maxval: 12)

a = Tendency.new(4.0);
z = 500.collect({arg i; a.at(i, \gamma)})
z.plot(discrete: true, minval: 0, maxval: 12)

a = Tendency.new(8.0);
z = 500.collect({arg i; a.at(i, \gamma)})
z.plot(discrete: true, minval: 0, maxval: 12)

// laplace
// 'high' value controls dispersion
a = Tendency.new(0.01);
z = 500.collect({arg i; a.at(i, \laplace)})
z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(0.1, 0);
z = 500.collect({arg i; a.at(i, \laplace)})
z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(1.0, 0);
z = 500.collect({arg i; a.at(i, \laplace)})
z.plot(discrete: true, minval: -3, maxval: 3)

// alaplace (anti-laplace)
// special case of laplace, creates a gap in the center
// 'high' value controls dispersion
a = Tendency.new(0.01);
z = 500.collect({arg i; a.at(i, \alaplace)})
z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(0.1);
z = 500.collect({arg i; a.at(i, \alaplace)})
z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(1.0, 0);
z = 500.collect({arg i; a.at(i, \alaplace)})
z.plot(discrete: true, minval: -3, maxval: 3)

// hcos
// hyperbolic cosine distribution
// 'high' value controls dispersion
a = Tendency.new(0.01);
z = 500.collect({arg i; a.at(i, \hcos)})
z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(0.1);
z = 500.collect({arg i; a.at(i, \hcos)})
z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(1.0);
z = 500.collect({arg i; a.at(i, \hcos)})
z.plot(discrete: true, minval: -3, maxval: 3)

// logistic distribution
// 'high' value controls dispersion
a = Tendency.new(0.01);
z = 500.collect({arg i; a.at(i, \logistic)})
z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(0.1);
z = 500.collect({arg i; a.at(i, \logistic)})
z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(1.0);
z = 500.collect({arg i; a.at(i, \logistic)})
z.plot(discrete: true, minval: -3, maxval: 3)

// poisson
// 'high' value is the mean of the distribution
// this distribution has a discrete histogram (not continuous)
// it returns always integer values
a = Tendency.new(4)
z = 500.collect({arg i; a.at(i, \poisson)})
z.plot(discrete: true)
z.histo.plot(discrete: true)

a = Tendency.new(6)
z = 500.collect({arg i; a.at(i, \poisson)})
z.plot(discrete: true)
z.histo.plot(discrete: true)

// arcsin
// arcsin distribution
// 'high' value controls dispersion (spread)
// output range is between 0 and this value
// histogram shape is similar to beta with parA=parB=0.5
a = Tendency.new(0.01);
z = 500.collect({arg i; a.at(i, \arcsin)})
z.maxItem;
z.plot(discrete: true, minval: 0, maxval: 10)
z.histo.plot(discrete: true)

a = Tendency.new(0.1);
z = 500.collect({arg i; a.at(i, \arcsin)})
z.maxItem;
z.plot(discrete: true, minval: 0, maxval: 1)

a = Tendency.new(1.0);
z = 500.collect({arg i; a.at(i, \arcsin)})
z.maxItem;
z.plot(discrete: true, minval: 0, maxval: 1)

// Symmetrical non-linear distributions

// beta 
// this distribution takes two extra parameters parA and parB
// to describe where the likelihood that a random value will occur 
// near high (parA) or low (parB)

// parA = parB = 0.5 
// histogram has symmetrical shape
a = Tendency.new(1.0, 0.0, 0.5, 0.5);
z = 500.collect({arg i; a.at(i, \betaRand)})
z.plot(discrete: true)
z.histo.plot(discrete: true)

// parA = 0.5, parB = 0.25 
// histogram lopsided towards high end
a = Tendency.new(1.0, 0.0, 0.5, 0.25);
z = 500.collect({arg i; a.at(i, \betaRand)})
z.plot(discrete: true)
z.histo.plot(discrete: true)


// parA = 0.25, parB = 0.5 
// histogram lopsided towards low end
a = Tendency.new(1.0, 0.0, 0.25, 0.5);
z = 500.collect({arg i; a.at(i, \betaRand)})
z.plot(discrete: true)
z.histo.plot(discrete: true)


// cauchy 
// this distribution has a symmetrical histogram around 0
// for this implementation 'high' controls its dispersion
// if parA = 1, only positive values are returned

// small dispersion around 0.0
a = Tendency.new(0.01)
z = 500.collect({arg i; a.at(i, \cauchy)})
z.plot(discrete: true, minval: -3, maxval: 3)

// larger dispersion around 0.0
a = Tendency.new(0.1)
z = 500.collect({arg i; a.at(i, \cauchy)})
z.plot(discrete: true, minval: -3, maxval: 3)

// even larger dispersion around 0.0, return only positive half
a = Tendency.new(1.0, parA: 1)
z = 500.collect({arg i; a.at(i, \cauchy)})
z.plot(discrete: true, minval: -3, maxval: 3)

// gaussian
// this distribution has a bell-shaped symmetrical histogram
// 'high' is the deviation or width of the bell

// small deviation
a = Tendency.new(0.01)
z = 500.collect({arg i; a.at(i, \gauss)})
z.plot(discrete: true, minval: -3, maxval: 3)


// larger deviation
a = Tendency.new(0.1)
z = 500.collect({arg i; a.at(i, \gauss)})
z.plot(discrete: true, minval: -3, maxval: 3)

// even larger deviation
a = Tendency.new(1.0)
z = 500.collect({arg i; a.at(i, \gauss)})
z.plot(discrete: true, minval: -3, maxval: 3)


// Using them with envelopes and time:

a = Tendency.new(Env([0.01, 1.0], [1]), 1.0);
// Tendency at takes a time for the Envs
z = 500.collect({arg i; a.at(i / 500, \gauss)})
z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(Env([0.01, 1.0], [1]));
z = 500.collect({arg i; a.at(i / 500, \arcsin)})
z.plot(discrete: true, minval: 0, maxval: 1)