Erlang RNG

[Namir]

This programs generates random numbers that are from teh Erlang PDF. The program uses the following algorithm:

Given parameters k (integer) and theta

S=0
For i = 1 to k
Generate u=U(0,1)
X = -1/Theta*ln(u)
S = S + X
End
Return S

Memory Map and Flags

R A = Theta
R B = k (integer)
R E = random number seed
R 0 = used
R 1 = S
R 2 = k counter
R I = loop counter

F 0 = When manually set, the program stops after calculating each exponenitally distributed number, after pressing [C]. When cleared, the program proceed in full speed after pressing [C] or after resuming the program by pressing [R/S].

Listing

Code:


1 LBL e        # Store seed
2 STO E
3 RTN

4 LBL E        # Calculate uniform random number
5 RCL E
6 PI
7 +
8 5
9 Y^X
10 FRC
11 STO E
12 RTN

13 LBL a
14 STO A        # Store theta
15 X<>Y
16 INT        # make sure argument is integer
17 STO B        # Stoer k
18 RTN

19 LBL A        # Calculate one Erlang random number
20 0
21 STO 1        # S = 0
22 RCL B
23 STO 2        # Store loop counter
24 LBL 2        # Start loop
25 GSB E
26 LN
27 CHS
28 RCL A
29 /        # calculate X = Exponential random number
30 STO+ 1        # S = S + X
31 1
32 STO- 2        # decrement counter
33 RCL 2
34 x>0?        # counter > 0?
35 GTO 2
36 RCL 1        # return s
37 RTN

38 LBL C        # Test mean and sdev for Erlang numbers
39 STI        # Store number of iterations
40 P<>S
41 0
42 STO 4
43 STO 5
44 STO 6
45 STO 7
46 STO 8
47 STO 9
48 P<>S        # Clear stat registers
49 LBL 0
50 RC I
51 PAUSE
52 GSB A
53 STO 0
54 F? 0
55 R/S
56 GSB A
57 F? 0
58 R/S
59 RCL 0
60 Sigma+
61 DSZ
62 GTO 0
63 x-bar        # view the averages
64 R/S
65 s        # view the standard deviations
66 R/S
67 RCL B
68 RCL A
69 /
70 R/S        # display expected mean
71 LAST X
72 /
73 SQRT        # display expected standard deviation
74 RTN

75 LBL c        # Store a sample of 20 Erlang distributed random numbers
76 1
77 9
78 STI        # Store number of iterations
79 LBL 1        # loop to generate and store the first 19 numbers
80 GSB A
81 STO (i)
82 DSZ
83 GTO 1
84 GSB A        # Generate and store the 20th random number
85 STO (i)
86 RTN

Usage

1. Enter initial/new random number seed and press [f][E].
2. Enter integer value for k, press [ENTER], enter value for theta, and press [f][A].
3. Enter the number of iterations and press [C]. The program will stop and display the averages for two sample sets. If flag 0 is set, the program will stop after calculating each random number. You must then press [R/S] to resume. You can clear flag 0 and then press [R/S] to resume the program at full speed.
4. Press [R/S] to view the standard deviations for the same two sample sets.
5. (optional) Press [E] to generate a uniform random number.
6. (optional) Press [A] to generate an Erlang random number.
7. (optional) Press [f][C] to generate a sample of 20 Exponenaially distributed random numbers that are store in registers R0 to R9 and Rs0 through Rs9.