Random Number Generation and Monte Carlo Methods

by James E. Gentle

Errata for Second Printing of First Edition

(see errata for first printing)

  • Page 10, Figure 1.2: (Thanks to Tom Yost!)
    Point 15 should be (22,4) and point 14 should be (28,22).

  • Page 10, line 10b:
    One of the duplicated 12's should be omitted.

  • Page 10, line 4b: (Thanks to Tom Yost!)
    The last number, 0.35, should be omitted.

  • Page 11, caption for Figure 1.3:
    Multiplier should be 12.

  • Page 34, line 9: (Thanks to Craig Borkowf!)
    Should be ``... the difference between two discrete uniforms modulo the larger of the ranges of the two random variables is also a discrete uniform.''

  • Page 49, line 8: (Thanks to Craig Borkowf!)
    Should be ``A good majorizing function would be such that $c$ is as small as possible. (The areas under $g$ and under $f$ are both 1.).''

  • Page 78, line 14: (Thanks to Craig Borkowf!)
    Instead of ``m(m-1)V/m'', should be ``(m-1)V/m''.

  • Page 83, line 6: (Thanks to Craig Borkowf!)
    Instead of ``nx + \beta - 1'', should be ``n - x + \beta - 1''.

  • Page 94, line 8b: (Thanks to Xiaohui Luo!)
    ``b = a + e^-ta/t'' should be ``b = 1 + e^-ta/t''.

  • Page 95, line 1: (Thanks to Xiaohui Luo!)
    Should be a minus sign in from of log.

  • Page 95, last two lines:
    ``x'' should be ``y''.

  • Page 97, t density: (Thanks to Gonno Leendertse!)
    There should be no ``$\sigma$'' in the expression for the density.

  • Page 98, line 9: (Thanks to James G. MacKinnon and to Gonno Leendertse!)
    The r in the denominator should be taken from under the square root sign.
    Alternatively (and this is the way the computations should be performed), ``r^2'' in lines 5 and 6 should be ``r'' (that is, r=v_1^2+v_2^) , and the exponent of r in the numerator under the square root sign should be ``-2/\nu'', instead of ``-4/\nu''.

  • Page 99, line 26:
    Should be ``... scaled by $\beta^{1/\alpha}$''.

  • Page 102, lines 29 through 31: (Thanks to Craig Borkowf!)
    The term in the denominator of the Rayleigh density should be $1/\sigma^2$, and the parenthetical remark should be ``which is a Weibull with parameters $\alpha=2$ and $\beta=2\sigma^2$''

  • Page 103, line 20:
    ``u_2'' should be in the denominator. The full expression should be
    x \leq \frac{t}{t-1}\frac{2^{a-1}-1}{2^{a-1}u_2}

  • Page 107, Algorithm 3.7, step 2: (Thanks to Zhenming Su and to Jan-Thijs van Kaam!)
    Should be ``For $i=1,2,\ldots,d$, generate independent chi-squared variates, $y_i$, with $n+1-i$ degrees of freedom.''

  • Page 111, lines 2 and 13: (Thanks to Craig Borkowf!)
    The limits on i and j should include all j when i<l, and j<m when i=l.

  • Page 114, line 24: (Thanks to Craig Borkowf!)
    In the second instance, should be $\alpha_{22}-\alpha_{12}$.

  • Page 121, at end of second paragrpah: (Thanks to Craig Borkowf!)
    ``n'' should be ``N''.

  • Page 127, line 2: (Thanks to Craig Borkowf!)
    ``\lambda(t)'' ahould be ``\lambda(t_i+d)''

  • Page 153, line 12: (Thanks to Craig Borkowf!)
    ``generator'' should be ``correlation''

  • Page 164, line 30: (Thanks to Craig Borkowf!)
    Should be 10 degrees of freedom.

  • Page 173, lines 14 and 15: (Thanks to Craig Borkowf!)
    Should be ``xx <- sample(massp, n, replace=T, probs)''.

  • Page 174, line 9b: (Thanks to Juan Antonio Caballero!)
    Should be 16/15 (which is 64/60, instead of 64/35)

  • Page 231: (Thanks to Juan Antonio Caballero!)
    The date of Joe Schafer's book is 1997.

    (Thanks also to Craig Borkowf and Juan Antonio Caballero for several additional comments.)