Generate Discrete Random Variable

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Contents

function [ar_drv_ele, ar_drv_prb] = fft_gen_discrete_var(varargin)

FFT_GEN_DISCRETE_VAR generate discrete random variables

could be interest rates. Given parameters, generate discrete random variable, translating to other level/units elsewhere potentially.

@st_drv_ele_type string scalar values associated with element of the sample space of the discrete random variable, possibilities are:

  1. unif: uniform between fl_max and fl_min, equi-distance.
  2. seg3: between fl_max and fl_min, three gaps, increasing for each segment, might not reach fl_max
  3. logspace: logspace function between fl_max and fl_min

@st_drv_prb_type string distributional functions, possibilities are:

  1. poiss: top truncated poisson distribution (non-symmetric, approximates exponential)
  2. binom: binomial (can be symmetric, approximates normal)
  3. unif: uniform distribution

@params_map container an container of parameters if the parameter is not covered by the explicitly named parameters

@return ar_drv_ele array discrete random variable outcomes

@return ar_drv_prb array discrete random variable probabilities

Parameters Defaults

bl_input_override = 0;
if (length(varargin) == 2)
    bl_input_override = varargin{2};
end

if (bl_input_override)

    [param_dsv_map, ~] = varargin{:};

    bl_display_dvg = false;

else

    param_dsv_map = containers.Map('KeyType','char', 'ValueType','any');

    param_dsv_map('fl_binom_p') = 0.25;
    param_dsv_map('fl_poiss_mean') = 5;
    param_dsv_map('fl_logspace_adj') = 0.075;

    param_dsv_map('st_drv_ele_type') = 'unif';
    param_dsv_map('st_drv_prb_type') = 'poiss';
    param_dsv_map('fl_max') = 0.095;
    param_dsv_map('fl_min') = 0.025;
    param_dsv_map('fl_n') = 5;

    bl_display_dvg = true;
end

Retrieve Parameters from Map

params_group = values(param_dsv_map, {'st_drv_ele_type', 'st_drv_prb_type', 'fl_max', 'fl_min', 'fl_n'});
[st_drv_ele_type, st_drv_prb_type, fl_max, fl_min, fl_n] = params_group{:};

Gereate Interest Rates Shocks

if (fl_max == fl_min)

Single Point Shock

    ar_drv_ele = linspace(fl_min, fl_max, 1);
    ar_drv_prb = zeros(size(ar_drv_ele)) + 1;

else

Multiple Points Shock

Discrete Outcomes: Uniform

    fl_gap = (fl_max - fl_min)/(fl_n-1);

    if (strcmp(st_drv_ele_type, 'unif'))
        ar_drv_ele = fl_min:fl_gap:fl_max;
    end

Discrete Outcomes: three segments of increasing gaps

    if (strcmp(st_drv_ele_type, 'seg3'))

        fl_most_least_gap = (fl_max - fl_min);
        fl_most_least_seg3_interval = fl_most_least_gap/3;

        ar_seg1 = fl_min:fl_gap:fl_most_least_seg3_interval;
        ar_seg2 = max(ar_seg1):(fl_gap*2):fl_most_least_seg3_interval*2;
        ar_seg3 = max(ar_seg2):(fl_gap*3):fl_max;

        ar_drv_ele =[ar_seg1, ar_seg2, ar_seg3];
    end

Discrete Outcomes: log space

    if (strcmp(st_drv_ele_type, 'logspace'))
        fl_logspace_adj = param_dsv_map('fl_logspace_adj');
        ar_drv_ele = logspace(log10(fl_min + fl_logspace_adj), ...
            log10(fl_max + fl_logspace_adj), fl_n) - fl_logspace_adj;
    end

Probability: Uniform

    if (strcmp(st_drv_prb_type, 'unif'))
        ar_drv_prb = zeros(size(ar_drv_ele)) + 1/length(ar_drv_ele);
    end

Probability: binom

    if (strcmp(st_drv_prb_type, 'binom'))
        fl_binom_p = param_dsv_map('fl_binom_p') ;
        it_poiss_n = length(ar_drv_ele)-1;
        ar_poiss_x = 0:1:it_poiss_n;
        ar_drv_prb = binopdf(ar_poiss_x, it_poiss_n, fl_binom_p);
    end

Probability: poisson

divide by sum because poisson max n is infinity

    if (strcmp(st_drv_prb_type, 'poiss'))
        fl_poiss_mean = param_dsv_map('fl_poiss_mean');
        it_poiss_n = length(ar_drv_ele)-1;
        ar_poiss_x = 0:1:it_poiss_n;
        ar_drv_prb = poisspdf(ar_poiss_x, fl_poiss_mean);
        ar_drv_prb = ar_drv_prb./sum(ar_drv_prb);
    end

end

Display

if (bl_display_dvg)
    disp('ar_drv_ele');
    disp(ar_drv_ele);
    disp('ar_drv_prb');
    disp(ar_drv_prb);
end

ar_drv_ele
    0.0250    0.0425    0.0600    0.0775    0.0950

ar_drv_prb
    0.0153    0.0765    0.1912    0.3187    0.3983


end

ans =

    0.0250    0.0425    0.0600    0.0775    0.0950


Published with MATLAB® R2019a