sumsmnw12 {lazy.irt} R Documentation

## Distribution of the Weighted Sum of Two Independent Scored Multinomial Distributions

### Description

Distribution of the Weighted Sum of Two Independent Scored Multinomial Distributions

### Usage

```sumsmnw12(p1, p2, w2 = 1, eps = 1e-08, print = 0)
```

### Arguments

 `p1` Probability of the fist random variable `p2` Probability of the second random variable `w2` Integer weight to the second random variable `eps` small number `print` = 1 to print result

### Details

This program calculats the distrobution of
X12 = X1 + w2 X2
where
Xi is distributed as Scored Multinomial with pi, i=1,2.
That is, this program calculates the probability that
p12[a] = Pr( X12 = a ) , a=0,1,..., n12=(n1-1)+w2*(n2-1)

Note
length(pi) = ni = #' of categories of the i-th r.v.
= mi + 1 where mi is the max score of the i-th r.v.

### Value

A matrix of (score, prob)

### References

Mayekawa, S., & Arai, S. (2008). Distribution of the Sum of Scored Multinomial Random Variables and Its Application to the Item Response Theory. In K. Shigemasu, A. Okada, T.Imaizumi, & T. Hoshino (Eds.) New Trends in Psychometrics. Tokyo: University Academic Press.

### Examples

```sumsmnw12( 1:3, 1:2, 2, print=1 )

```

[Package lazy.irt version 0.1.3 Index]