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stats/base/distribution  - statistical distributions

 binomialdist v discrete values for binomial distribution binomialprob v probability of success in binomial distribution chisqcdf v chi squared CDF normalcdf v normal distribution (0,1) CDF normalprob v probability of success in normal distribution poissondist v discrete values for poisson distribution poissonprob v probability of success in poisson distribution

### binomialdist

binomialdist (v) discrete values for binomial distribution

```y has 2 elements p,n:
0  =  probability of success in one trial
1  =  number of trials

E=n*p, var=n*p*-.p

e.g.  binomialdist 0.25 5  ...distribution of results from 0 to 5
```

### binomialprob

binomialprob (v) probability of success in binomial distribution

```y has 3 or 4 elements:
0  =  probability of success in one trial
1  =  number of trials
2  =  minimum number of successes
{3} =  maximum number of successes

e.g.  binomialprob 0.25 100 30 40    ...probability that there are
between 30 and 40 successes in 100 trials, where probability = 0.25
```

### chisqcdf

chisqcdf (v) chi squared CDF

```chi squared cumulative distribution function
see wiki Essays/Chi_Squared_CDF
```

### normalcdf

normalcdf (v) normal distribution (0,1) CDF

```normal(0,1) cumulative distribution function
see wiki Essays/Normal_CDF

the following are equivalent, but normalcdf more accurate:
normalcdf X
1 - normalprob 0 1, X
```

### normalprob

normalprob (v) probability of success in normal distribution

```y has 3 or 4 elements:
0  =  mean of distribution
1  =  standard deviation
2  =  minimum result
{3} =  maximum result

e.g.  normalprob 0 1 2    ...probability that result will be
greater than 2, where mean = 0, standard deviation 1

Result is rounded to 7 decimal places
Algorithm has accuracy ~ 7.5*1e_8
```

### poissondist

poissondist (v) discrete values for poisson distribution

```y has 2 elements:
0 = mean of distribution
1 = maximum value to show

e.g.  poissondist 2 10
= list of probabilities of values from 0 to 10
in poisson distribution of mean 2
```

### poissonprob

poissonprob (v) probability of success in poisson distribution

```y has 2 or 3 elements:
0   =  mean of distribution
1   =  minimum number of successes
{2} =  maximum number of successes

e.g.
poissonprob 5 4 7    ...probability that result will be
between 4 and 7 inclusive, where mean result is 5.
poissonprob 5 6 6    ...probability that result will be
exactly 6, where mean result is 5.
```