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 | :: Normal CDF - Free Statistics Software (Calculator) :: | |
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All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.
This free online software (calculator) computes the area under the normal density for a given one-sided or two-sided quantile value (Z-score), mean, and standard deviation. These computed probabilities are often displayed (in statistics handbooks) in the form of the so-called statistical tables about the normal distribution.
In addition, if a probability is specified, the software computes the quantiles (Z-scores) that correspond to the area under the normal density function.
You must enter (at least) a quantile value, or a probability value. You are allowed to enter both (the Z-score and the probability) at the same time.
Click here to edit the underlying code of this R Module.Click here to edit the underlying code of this R Module.
| Cite this software as: | | Wessa P., (2008), Normal CDF (v1.0.9), Free Statistics Software (v1.1.22-r6), Office for Research Development and Education, URL http://www.wessa.net/rwasp_cdfnorm.wasp/ | | | The R code is based on : | | | Becker, R. A., Chambers, J. M. and Wilks, A. R., (1988), The New S Language, Wadsworth & Brooks/Cole.
| | | Wichura, M. J. (1988) Algorithm AS 241: The Percentage Points of the Normal Distribution, Applied Statistics, vol. 37, 477-484.
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| Source code of R module | | 1 | par2 <- as.numeric(par2) | | 2 | par3 <- as.numeric(par3) | | 3 | if (par3 <= 0) par3 = 1 | | 4 | if (par1 != "") { | | 5 | par1 <- as.numeric(par1) | | 6 | oldpar1 <- par1 | | 7 | par1 <- (par1 - par2) / par3 | | 8 | r <- pnorm(par1) | | 9 | ru <- pnorm(par1,lower.tail=F) | | 10 | rb <- pnorm(abs(par1)) - pnorm(-abs(par1)) | | 11 | } | | 12 | r | | 13 | ru | | 14 | rb | | 15 | if (par4 != "") { | | 16 | par4 <- as.numeric(par4) | | 17 | q1 <- qnorm(par4,par2,par3) | | 18 | q1u <- qnorm(par4,par2,par3,lower.tail=F) | | 19 | q2 <- qnorm((1-par4)/2,par2,par3,lower.tail=F) | | 20 | } | | 21 | q1 | | 22 | q1u | | 23 | q2 | | 24 | load(file="createtable") | | 25 | a<-table.start() | | 26 | a<-table.row.start(a) | | 27 | a<-table.element(a,"Normal Density Function",2,TRUE) | | 28 | a<-table.row.end(a) | | 29 | a<-table.row.start(a) | | 30 | a<-table.element(a,"mean",header=TRUE) | | 31 | a<-table.element(a,par2) | | 32 | a<-table.row.end(a) | | 33 | a<-table.row.start(a) | | 34 | a<-table.element(a,"standard deviation",header=TRUE) | | 35 | a<-table.element(a,par3) | | 36 | a<-table.row.end(a) | | 37 | if (par1 != "") { | | 38 | a<-table.element(a,"Area under Normal Density",2,TRUE) | | 39 | a<-table.row.end(a) | | 40 | a<-table.row.start(a) | | 41 | a<-table.element(a,"q value",header=TRUE) | | 42 | a<-table.element(a,oldpar1) | | 43 | a<-table.row.end(a) | | 44 | a<-table.row.start(a) | | 45 | a<-table.element(a,"z value",header=TRUE) | | 46 | a<-table.element(a,par1) | | 47 | a<-table.row.end(a) | | 48 | a<-table.row.start(a) | | 49 | a<-table.element(a,"P[X <= z]",header=TRUE) | | 50 | a<-table.element(a,r) | | 51 | a<-table.row.end(a) | | 52 | a<-table.row.start(a) | | 53 | a<-table.element(a,"P[X > z]",header=TRUE) | | 54 | a<-table.element(a,ru) | | 55 | a<-table.row.end(a) | | 56 | a<-table.row.start(a) | | 57 | a<-table.element(a,"P[-|z| <= X <= |z|]",header=TRUE) | | 58 | a<-table.element(a,rb) | | 59 | a<-table.row.end(a) | | 60 | a<-table.row.start(a) | | 61 | a<-table.element(a,"P[-|z| <= X] + P[X > |z|]",header=TRUE) | | 62 | a<-table.element(a,1-rb) | | 63 | a<-table.row.end(a) | | 64 | } | | 65 | if (par4 != "") { | | 66 | a<-table.element(a,"Quantiles",2,TRUE) | | 67 | a<-table.row.end(a) | | 68 | a<-table.row.start(a) | | 69 | dum <- paste("q given P[X <= q] = ",par4,sep="") | | 70 | a<-table.element(a,dum,header=TRUE) | | 71 | a<-table.element(a,q1) | | 72 | a<-table.row.end(a) | | 73 | a<-table.row.start(a) | | 74 | dum <- paste("q given P[X > q] = ",par4,sep="") | | 75 | a<-table.element(a,dum,header=TRUE) | | 76 | a<-table.element(a,q1u) | | 77 | a<-table.row.end(a) | | 78 | a<-table.row.start(a) | | 79 | dum <- paste("|q| given P[-|q| <= X] + P[X > |q|] = ",1-par4,sep="") | | 80 | a<-table.element(a,dum,header=TRUE) | | 81 | a<-table.element(a,q2) | | 82 | a<-table.row.end(a) | | 83 | } | | 84 | a<-table.end(a) | | 85 | table.save(a,file="mytable.tab") |
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To cite Wessa.net in publications use:
Wessa, P. (2008), Free Statistics Software, Office for Research Development and Education,
version 1.1.22-r6, URL http://www.wessa.net/
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