Reliability/Survival Software Engines                        
Probability Distribution Function Input Automatic Output and Charts
PDF PDF Name PDF Type Alternative Name PDF Bank Number of PDF Parameters Random or Time Variables Probability Distribution Function Reliability / Survival Unreliability Failure / Hazard Rate Cumulative Hazard Function Conditional Reliability / Survival Conditional Unreliability Probability of Failure During Mission
Worksheet Parametric Model Version or Model Name/Category/Subfamilies Workbook   Age at Start of Mission Mission Time f(T) and
R(T) and
Q(T) and
λ(T) and
H(T) and
R(T,t) Q(T,t) Q(T+t)-Q(T)
1 8020.D α%-(1-α%) Rule Discrete Includes 80%-20% Rule Discrete 1 T t
2 AMO Amoroso Generalized Distribution Hierarchy Distribution Subfamilies: Stacy (Generalized Gamma/Inverse Gamma), Stretched Exponential; Gamma, Wilson-Hilferty, Pearson Type III, Exponential, Shifted Exponential, Half-Normal, Nakagami, Chi-Square, Scaled-Chi-Square, Chi, Scaled-Chi, Rayleigh, Maxwell; Pearson Type V, Inverse Gamma, Inverse Exponential, Lévy, Scaled Inverse Chi-Square, Inverse-Chi Square, Scaled Inverse-Chi, Inverse-Chi, Inverse Rayleigh; Generalized Fisher-Tippett, Fisher-Tippett (Generalized Extreme Value), Weibull, Generalized Weibull, Fréchet, Generalized Fréchet4 PDF-A 4 T t
3 BETA Beta   Euler Beta of the First Kind; Pearson Type I PDF-B 2 T t
4 BETA4 Beta     PDF-B 4 T t
5 BETAP Beta Prime   Pearson Type VI; Inverted Beta; Beta Distribution of the 2nd Kind PDF-B 4 T t
6 BIN.D Binomial Discrete   Discrete 2 T t
7 BRAD Bradford   Bradford Law of Scattering PDF-B 3 T t
8 BS Birnbaum-Saunders   Fatigue Life PDF-B 3 T t
9 BUR1 Burr XVII Singh-Maddala; Generalized Log-Logistic PDF-B 2 T t
10 BUR2 Burr XVII Transformed Pareto PDF-B 3 T t
11 BUR3 Burr XVII   PDF-B 3 T t
12 BUR4 Burr XVII   PDF-B 4 T t
13 CAU Cauchy     PDF-C 2 T t
14 CAUT Doubly Truncated Cauchy     PDF-C 4 T t
15 CHI Chi     PDF-C 1 T t
16 CHI3 Chi     PDF-C 3 T t
17 CHIS Chi-Square Standard   PDF-C 1 T t
18 CHIS3 Chi-Square     PDF-C 3 T t
19 DAG Dagum     PDF-D 3 T t
20 DAG1 Dagum 1   PDF-D 3 T t
21 DAGIB Dagum   Inverse Burr; Kappa PDF-D 4 T t
22 EV1MAX Extreme Value for Maxima 1 Gumbell PDF-E 2 T t
23 EV1MIN Extreme Value for Minima 1   PDF-E 2 T t
24 EV2MAX Extreme Value for Maxima 2 Fréchet; Reversed Weibull PDF-E 3 T t
25 EV2MIN Extreme Value for Minima 2   PDF-E 3 T t
26 EV3MAX Extreme Value for Maxima 3   PDF-E 3 T t
27 EV3MIN Extreme Value for Minima 3 Weibull PDF-E 3 T t
28 EXP Exponential     PDF-E 2 T t
29 EXPL Exponential-Logarithmic     PDF-E 2 T t
30 F F-Distribution Standard Fisher-Snedecor PDF-F 2 T t
31 F4 F-Distribution   Fisher-Snedecor PDF-F 4 T t
32 FP Feller-Pareto Generalized Distribution Hierarchy Distribution Subfamilies: Pareto; Transformed Beta (Burr, Log-Logistic, Paralogistic); Generalized Pareto (Scaled-F, Inverse Pareto); Inverse Burr (Log-Logistic, Inverse Pareto, Inverse Paralogistic)5 PDF-F 5 T t
33 FT Fisher-Tippett   Generalized Extreme Value (GEV); von Mises-Jenkinson; von Mises Extreme Value4 PDF-F 3 T t
34 GAM Gamma   Pearson Type III PDF-G 3 T t
35 GBUR Generalized Burr     PDF-G 5 T t
36 GEO.D Geometric Discrete   Discrete 1 T t
37 GEV Generalized Extreme Value Generalized Distribution Hierarchy Fisher-Tippett Distribution; Distribution Subfamilies4,6: Gumbell, Fréchet, and Reversed Weibull (Extreme Value Distributions Types I, II, and III)6 PDF-G 3 T t
38 GFRE Generalized Fréchet     PDF-G 4 T t
39 GFT Generalized Fisher-Tippett     PDF-G 4 T t
40 GGAM Generalized Gamma     PDF-G 4 T t
41 GLOG Generalized Logistic     PDF-G 3 T t
42 GLOG7 Generalized Logistic Generalized Distribution Hierarchy Generalized Logistic Distribution Subfamilies7: Ojo-Olapade (6 Parameters); Wu et al. (5 Parameters); George-Ojo (4 Parameters); Extended Types I, II (4 Parameters); Balakrishnan-Leung Types I, II, III (3 Parameters); Berkson (2 Parameters); Located/Scaled (1 Parameter); Standard (0 Parameters) PDF-G 7 T t
42 GMAK Generalized Makeham   Kosznik-Biernacka PDF-G 3 T t
43 GN1 Generalized Normal 1   PDF-G 3 T t
44 GN2 Generalized Normal 2   PDF-G 3 T t
45 GOM Gompertz     PDF-G 2 T t
46 GP Generalized Pareto     PDF-G 3 T t
47 GPB2 Generalized Pareto   Beta of the Second Kind PDF-G 3 T t
48 GW Generalized Weibull     PDF-G 4 T t
49 GY.D Generalized Yule Discrete   Discrete 2 T t
50 HGEO.D Hpypergeometric Discrete   Discrete 3 T t
51 HS Hyperbolic Secant     PDF-H 2 T t
52 HYPER Hyperexponential     PDF-H 10 T t
53 HYPO Hypoexponential     PDF-H 5 T t
54 IGAM Inverse Gamma   Vinci PDF-I 2 T t
55 IGAMPV Inverse Gamma   Pearson Type V PDF-I 3 T t
56 IGAUS Inverse Gaussian   Inverse Normal - Schrödinger-Wald PDF-I 2 T t
57 IPL Inverse Paralogistic     PDF-I 2 T t
58 JSU Johnson Unbounded     PDF-J 4 T t
59 JSB Johnson Bounded     PDF-J 4 T t
60 KUM Kumaraswamy Doubly Bounded     PDF-K 2 T t
61 KUM4 Kumaraswamy Doubly Bounded     PDF-K 4 T t
62 L Logarithmic     PDF-L 2 T t
63 LAP Laplace     PDF-L 2 T t
64 LEV Lévy   Van Der Waals Profile PDF-L 2 T t
65 LEXP Linear Exponential     PDF-L 2 T t
66 LLAP Log-Laplace   Double Pareto PDF-L 3 T t
67 LLOG Log-Logistic   Fisk PDF-L 3 T t
68 LN LogNormal     PDF-L 2 T t
69 LOG Logistic     PDF-L 2 T t
70 LOM Lomax   Pareto-Lomax PDF-L 2 T t
71 LS.D Log-Series Discrete Logarithmic Discrete 1 T t
72 MAK Makeham     PDF-M 3 T t
73 MIX3 Multiple Failure Modes Mixture Mixed Population Model (1-3 Subpopulations) PDF-M 3 T t
74 MIX6 Multiple Failure Modes Mixture Mixed Population Model (1-6 Subpopulations) PDF-M 5 T t
75 NAK Nakagami-m   Fading Model PDF-N 2 T t
76 NAKGN Nakagami   Generalized Normal PDF-N 3 T t
77 N Normal   Gaussian; Bell Curve; Pearson Type V PDF-N 2 T t
78 NT Doubly Truncated Normal     PDF-N 4 T t
79 NTL Left Truncated Normal     PDF-N 3 T t
80 NTR Right Truncated Normal     PDF-N 3 T t
81 NBIN.D Negative Binomial Discrete Pascal Discrete 2 T t
82 PIII Pearson III   PDF-P 3 T t
83 P1 Pareto 1     PDF-P 2 T t
84 P2 Pareto 2     PDF-P 3 T t
85 P3 Pareto 3     PDF-P 3 T t
86 P4 Pareto 4     PDF-P 4 T t
87 PB Bounded Pareto     PDF-P 3 T t
88 PERT PERT Standard   PDF-P 3 T t
89 PERTV PERT Modified Vose PDF-P 4 T t
90 PL Paralogistic     PDF-P 2 T t
91 PN Power Normal     PDF-P 3 T t
92 POI.D Poisson Discrete   Discrete 1 T t
93 RAY Rayleigh     PDF-R 1 T t
94 RBT1 Reliability Bathtub 1 Dhillon PDF-R 2 T t
95 RBT2 Reliability Bathtub 2 Hjorth PDF-R 3 T t
96 RBT3 Reliability Bathtub 3 Govil-Aggarwal PDF-R 6 T t
97 RBT4 Reliability Bathtub 4 Dhillon PDF-R 5 T t
98 SGEO.D Shifted Geometric Discrete   Discrete 1 T t
99 SGOMP Shifted Gompertz     PDF-S 2 T t
100 SIL Siler   Siler Competing Hazards Model PDF-S 5 T t
101 SLLOG Shifted Log-Logistic   Generalized Log-Logistic PDF-S 3 T t
102 STACY Stacy   Distribution Subfamilies: Generalized Gamma; Generalized Inverse Gamma4 PDF-S 3 T t
103 SUNI.D Step Uniform Discrete   Discrete 3 T t
104 T Student t Standard Gosset; Pearson Type IV PDF-T 1 T t
105 T3 Student t     PDF-T 3 T t
106 TB Transformed Beta     PDF-T 4 T t
107 TRI Triangular     PDF-T 3 T t
108 UNI Uniform     PDF-U 2 T t
109 UNI.D Uniform Discrete   Discrete 2 T t
110 UQ U-Quadratic     PDF-U 2 T t
111 WEI Weibull   Extreme Value Type III; Fisher-Tippett Type III; Gumbel Type III PDF-W 3 T t
112 WEIL Weibull-Logarithmic   Ciumara-Preda PDF-W 3 T t
113 WH Wilson-Hilferty     PDF-W 2 T t
114 WO Wearout Life   Zacks PDF-W 3 T t
115 YS.D Yule-Simon Discrete   Discrete 1 T t
116 ZIPF.D Zipf's Law Discrete   Discrete 2 T t
117 ZM.D Zipf-Mandelbrot Law Discrete   Discrete 3 T t
1 Probability Density Function (PDF).
2 Cumulative Distribution Function (CDF) (Upper/Lower). Reliability=Upper CDF; Unreliability=Lower CDF.
4 PDF Banks: Continuous PDFs, organized alphabetically in workbooks PDF-A through PDF-Z; Discrete PDFs in workbook PDF-Discrete.
4 Gavin E. Crooks, The Amoroso Distribution. Lawrence Berkeley National Laboratory, U.S. Department of Energy, Tech. Note 003v4 (2010-01-14), See also arXiv:1005.3274v1 [math.ST] 18 May 2010,
5 S. Tahmasebi and J. Behboodian, Shannon Entropy for the Feller-Paret (FP) Family and Order Statistics of FP Subfamilies. Applied Mathematical Sciences, Vol. 4, 2010, no. 10, 495-505,
6 Generalized Extreme Value Distribution (GEV). Wikipedia, 21-Apr-2010,
PDF Bank PDF Type Number of PDFs Automatic Output Functions/Charts
A-Z Continuous 104 1,352
Discrete Discrete 14 182
All Continuous and Discrete 118 1,534
Macroknow probability distributions are used in many fields: engineering, finance, commerce, industry, military, medical, information science, research, etc. Industries where statistical techniques are extremely useful include manufacturing (automotive, aerospace, electronics), chemical process plants, energy (power generation, nuclear, oil, gas), transportation (airlines, railways), medical (pharmaceutical, hospitals), finance (banking, insurance), security, and defense. Applications include: reliability engineering, event tree analysis, fault tree analysis, attack tree analysis, survival data analysis, expert systems, insurance, actuarial science, and demographics. Depending on the probability distribution, input variables can include, one or more location, scale, and shape parameters. The input random variables for the probability distributions are the age T of a physical or biological unit and a mission time or life period t. The physical unit can be a system, a device, a component, or a part (mechanical, electrical, or electronic). The biological unit can be a human, a patient, an animal, or a living cell. The output variables include: the probability density function (PDF), the upper cumulative distribution function (reliability or survival function), the lower cumulative distribution function (CDF) (unreliability or death function), the hazard rate (failure rate or force of mortality), the cumulative hazard function, the conditional reliability or survival function, and the conditional unreliability or death function. In engineering, the conditional reliability is the probability that the physical unit will continue to operate during the mission time t, given that it has already operated for a time T. In medical or actuarial applications, the conditional survival is the probability that a person aged T, survives an additional time period t. All output variables are graphed automatically.
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