Techniques of exploratory data analysis are used in the construction of simple approximations for the percentage points of the chi-square distribution. The approximations are direct functions of the degrees of freedom and the tail probability. They are more accurate than Hoaglin's approximations.

In contrast to the usual approach of using a normalizing transformation, a direct approximation for the percentiles of the t distribution is developed by using techniques of exploratory data analysis. The approximation is convenient to use and has sufficient accuracy for many applications of the t distribution.

This paper gives fast and reliable algorithms for the numerical evaluation of the incomplete gamma functions and for auxiliary functions, such as functions related with the gamma function and error function. All these functions are of basic importance in applied probability problems.

In asynchronous transfer mode (ATM), networks, buffering is required to reduce cell loss and increase bandwidth utilization by the bursty traffic. Several types of traffic with different performance requirements on delay and loss will share buffer resources. We focus on the fully shared buffer with push-out and a randomized service priority rule. Some conservation relations are obtained which can be used to tune the parameters of the buffering and service disciplines.

The following corrections for “A Globally Gated Polling System with Server Interruptions, and Applications to the Repairman Problem” by O.J. Boxma, J.A. Weststrate, and U. Yechiali, which appeared in Volume 7, Number 2, of Probability in the Engineering and Informational Sciences, missed the press date.

p. 192, (3.3): Xi should be Xi

p. 194, (3.12):should be

p. 195, (4.1): N should be n in the five summations over n (15x)

p. 195, (4.2): should be moved to the next line (after the multiplication sign)

p. 195, below (4.3): Add: so that EY1m = EXm = λmEC

p. 195, (4.4): Add: for m < n

p. 195, I. –3: Add: for m < n

p. 196, (4.5): Add: for m < n

p. 196, I. 5: Add: Again cov(Xm, Xn) = λm λn var(C), independent of the server interruption process.

p. 196, (4.8): m ≤ n should be m < n

p. 197, 1st formula: [λi should be

p. 199, I. 6: 5.2 The should be The

p. 199, I. 14: 5.3 The should be The

p. 200, I. 10: [E should be E(

p. 204: The last line of subsection 6.2 should be changed to: Moreover, when sj → 0, the index rules (6.2) and (6.4) approach the well-known cμ rule in both the static and dynamic optimization.

p. 207, I. –1: (to appear) should be: 85–90

p. 208, I. 1: 92 should be 93 (2×)

p. 208, I. 5: (to appear) should be 35: 187–208