D STEPS Analysis of Real-World Data in Iran by the Persian Curve (PC)

1. Data Definition

The dataset is as follows: Real-World Data PERSIA002S5 Set 282 106 (1) Data RWD0010 (D STEP 01 TO D STEP 07):

105, 193, 211, 236, 302, 363, 389, 390, 391, 403, 530, 604, 605, 630, 716, 718, 727, 731, 749, 769, 770, 789, 804, 810, 811, 833, 868, 871, 875, 893, 897, 901, 906, 907, 919, 923, 931, 940, 957, 958, 961, 962, 974, 979, 982, 1001, 1008, 1010, 1011, 1012, 1014, 1017, 1032, 1039, 1045, 1046, 1047, 1057, 1063, 1070, 1073, 1076, 1085, 1090, 1094, 1099, 1107, 1119, 1120, 1128, 1129, 1131, 1133, 1136, 1138, 1144, 1149, 1160, 1166, 1170, 1173, 1181, 1183, 1188, 1190, 1203, 1206, 1209, 1218, 1220, 1221, 1228, 1230, 1231, 1233, 1239, 1244, 1258, 1268, 1294, 1316, 1327, 1328, 1369, 1393, 1435

2. Binning Parameters

The minimum (Min), maximum (Max), and bin edges are defined as: Min = 105, Max = 1435 Bins: 0, 220, 440, 660, 880, 1100, 1320, 1540, 1760

3. State Variable for Histogram, Frequency (Histogram), and Scaled Histogram

• State Variable for Histogram (100SH): 0, 13, 25, 38, 50, 63, 75, 88, 100
• Frequencies (Fre): 0, 3, 7, 4, 15, 37, 35, 5, 0
• 100Hist: 0, 2, 4, 2, 8, 21, 20, 3, 0

4. State Variable for Cumulative Data, Cumulative Data, and Scaled Cumulative Data

• Scaled Cumulative (100SC): 0, 14, 29, 43, 57, 71, 86, 100
• Cumulative Data (CUM): 0, 3, 10, 14, 29, 66, 101, 106
• 100CD(RWD0010): 0, 3, 9, 13, 27, 62, 95, 100

5. Plotting the Persian Curve (PC)

• The scaled histogram (Hist) and scaled cumulative data (CD) are plotted on a (0-1)×(0-1) graph, with:
  • PC (ordinate, y-axis)
  • State variable (abscissa, x-axis)

6. Key Points Selection

• 100(S) = SO, SN, SM, ST = 0, 25, 50, 100
• 100(PK) = PO, PN, PM, PT = 0, 8, 38, 100

7. Control Parameters Calculation

• 100aM = 100(38−0)(100−38)= 61
• 100b = 100log(7/61)/log(0.1716)= 111

8. Persian Curve (PC) Definition & Plotting

4(D;O)=2+(−;+)(1−6s^2+4s^3+cos(Pi*s))

PC=(PO*O^b+PT*aM*D^b)/(O^b+aM*D^b) ​

9. Density (PZ) Calculation & Plotting

PZ=cZ*(b*aM*D^(b−1)*O^(b−1)*(dD/ds))/(O^b+aM*D^b)^2 ​

10. Inverse of PC (Quantile SC) Determination

cos(Pi*SC) = (aM^(1/b)−aC^(1/b))/ ​(aM^(1/b)+aC^(1/b))

The Persian (Probability) Curve (PC) is proposed as a happy ending for developments in the Probability Theory. The PC is a certain, simple and universal tool for analysis of real-world data in various branches of human knowledge. All academics are invited to test and use the PC in place of conventional ones.

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