r:probability
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r:probability [2016/10/19 10:59] – [Converting Probabilities to Quantiles] hkimscil | r:probability [2019/10/04 10:27] (current) – [qt, pt] hkimscil | ||
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+ | ====== Normal distribution functions ====== | ||
^ Function | ^ Function | ||
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| Weibull | | Weibull | ||
| Wilcoxon | | Wilcoxon | ||
+ | ===== pnorm, qnorm ===== | ||
+ | |||
+ | <WRAP info> | ||
+ | Normal distribution | ||
+ | $ f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{\frac{-(x-\mu)^2}{2\sigma^2}} $ | ||
+ | |||
+ | Assume that the test scores of a college entrance exam fits a normal distribution. Furthermore, | ||
+ | |||
+ | < | ||
+ | [1] 0.5 | ||
+ | |||
+ | > pnorm(1.96) | ||
+ | [1] 0.9750021 | ||
+ | |||
+ | > pnorm(1.96)-pnorm(-1.96) | ||
+ | [1] 0.9500042 | ||
+ | |||
+ | > pnorm(c(1.96, | ||
+ | [1] 0.9750021 0.0249979 | ||
+ | |||
+ | > pnorm(84, mean=72, sd=15.2, lower.tail=FALSE) | ||
+ | [1] .2149176 | ||
+ | |||
+ | > qnorm(.2149176, | ||
+ | [1] 84 | ||
+ | </ | ||
+ | ===== rnorm ===== | ||
+ | Random samples from a normal distribution | ||
+ | < | ||
+ | > rnorm(50) | ||
+ | [1] -0.778662882 -0.389476396 -2.033798329 -0.982373104 | ||
+ | [6] -2.103864629 -0.381418049 | ||
+ | [11] -1.879263193 -1.239189026 | ||
+ | [16] 1.795551228 -1.322138481 -0.276086413 -0.743976510 -1.070050125 | ||
+ | [21] -0.349525474 | ||
+ | [26] -0.538926447 | ||
+ | [31] -0.664914510 | ||
+ | [36] -0.268632965 | ||
+ | [41] -0.153716777 | ||
+ | [46] 0.603955311 -0.568653469 -0.891303117 -2.525145692 | ||
+ | |||
+ | |||
+ | ===== qt, pt ===== | ||
+ | |||
+ | <WRAP info> | ||
+ | $t = \frac{Z}{\sqrt{\frac{V}{m}}}$ | ||
+ | < | ||
+ | [1] -2.5706 | ||
+ | |||
+ | > qt(c(0.025, 0.975), df=10) | ||
+ | [1] -2.228139 | ||
+ | |||
+ | > qt(c(0.025, 0.975), df=20) | ||
+ | [1] -2.085963 | ||
+ | |||
+ | > qt(c(0.025, 0.975), df=30) | ||
+ | [1] -2.042272 | ||
+ | |||
+ | > qt(c(0.025, 0.975), df=40) | ||
+ | [1] -2.021075 | ||
+ | |||
+ | > qt(c(0.025, 0.975), df=50) | ||
+ | [1] -2.008559 | ||
+ | |||
+ | . . . . . . | ||
+ | |||
+ | > qt(c(0.025, 0.975), df=50000) | ||
+ | [1] -1.960011 | ||
+ | |||
+ | </ | ||
+ | </ | ||
====== Counting the Number of Combinations ====== | ====== Counting the Number of Combinations ====== | ||
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</ | </ | ||
- | < | + | |
+ | < | ||
[1] -11.195667 | [1] -11.195667 | ||
</ | </ | ||
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Replacement in random sampling: Specify replace=TRUE to sample with replacement. | Replacement in random sampling: Specify replace=TRUE to sample with replacement. | ||
+ | |||
+ | < | ||
+ | sample(world.series$year, | ||
+ | [1] 1906 1963 1966 1928 1905 1924 1961 1959 1927 1934 | ||
+ | set.seed(121) | ||
+ | sample(world.series$year, | ||
+ | [1] 1906 1963 1966 1928 1905 1924 1961 1959 1927 1934 | ||
+ | </ | ||
+ | |||
====== Generating Random Sequences ====== | ====== Generating Random Sequences ====== | ||
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</ | </ | ||
- | < | + | < |
[1] -1.959964 | [1] -1.959964 | ||
</ | </ |
r/probability.1476844155.txt.gz · Last modified: 2016/10/19 10:59 by hkimscil