;+ ; NAME: ; PROBHEXP ; ; PURPOSE: ; This function determines the probability function of the binned ; waiting times between successive events for a hyperexponential ; distribution distorted by a non-extended dead time, ; ; f(t) = P1*r1*exp(-r1*(t-tau)) + (1-P1)*r2*exp(-r2*(t-tau)) ; ; CATEGORY: ; Math. ; ; CALLING SEQUENCE: ; ; Result = PROBHEXP( Wtmax, Mean1, Mean2, Offset, Prob1 ) ; ; INPUTS: ; Wt: An array of waiting times or the maximum waiting time to ; determine the probability density function at. ; ; Mean1: The average waiting time for the FIRST exponential. ; ; Mean2: The average waiting time for the SECOND exponential. ; ; Offset: The non-extended dead time. ; ; Prob1: Probability of generating events from the FIRST exponential. ; ; OPTIONAL INPUT KEYWORD PARAMETERS: ; ; BIN: Time resolution of the waiting times, (1=Default). ; ; OUTPUTS: ; This function returns the probabilities at the waiting times ; specified by the Wt parameter if Wt is an array. If Wt is a scalar, ; the waiting times chosen are [0, BIN, 2*BIN, 3*BIN,... N*BIN < Wt]. ; NOTE: To calculate the probability, one must take into account that ; events can fall anywhere within the time resolution, BIN. ; ; EXAMPLE: ; For times binned with a bin time interval of 1, then the possible ; binned waiting times are [0,1,2..] corresponding to REAL waiting ; times of ([0,1], [0,2], [1,3], ...]. If we want to determine the ; probabilities of binned waiting times of [0,10] when the average ; number of counts = 1/bin (without dead time) and the deadtime ; is 2.5, with 15% of the photons being affected by this ; software/hardware bug with a scale factor or 2, then ; ; avg_cts = 1.0 ; avg_cts2 = 0.5 ; tavg = 1./avg_cts ; tavg2 = 1./avg_cts2 ; dead_time = 2.5 ; max_waiting_time = 10 ; fraction_unaffected = 0.15 ; Probs = PROBHEXP( max_waiting_time, tavg, tavg2, ; dead_time, fraction_unaffected ) ; ; MODIFICATION HISTORY: ; Written by: Han Wen, October 1996. ; 06-DEC-1996 Renamed from PROBWBUG -> PROBHEXP, Changed Frac -> ; (1 - Prob1). ;- function PROBHEXP, Wt, Mean1, Mean2, Offset, Prob1, BIN=Bin NP = N_PARAMS() if (NP ne 5) then message, \$ 'Must be called with 5 parameters: Wt, Mean1, Mean2, Offset, Prob1' p1 = PROBEXP( Wt, Mean1, Offset, BIN=Bin ) p2 = PROBEXP( Wt, Mean2, Offset, BIN=Bin ) return, Prob1*p1 + (1-Prob1)*p2 end