Statistica Neerlandica

Es, A.J. Van; Gill, R.D.; Putten, C. Van

doi: 10.1111/j.1467-9574.1983.tb00805.xpmid: N/A

Abstract Some theory of linear congruential pseudo random number generators xn+1= (axn+c) mod m is summarized for the case in which the modulus m is a power of 10. These generators are especially suitable for implementation on both programmable and non‐programmable pocket calculators. Results are presented of extensive statistical testing of two specific generators.

Kardaun, O.

doi: 10.1111/j.1467-9574.1983.tb00806.xpmid: N/A

Abstract This paper deals with a concrete case: Of 90 male larynx‐cancer patients, diagnosed and treated in the period 1970–1978, either the survival time or, if the patient was still alive at the end of the study, an appropriate lower bound on it was recorded. One factor (stage of the cancer) and one covariate (age of the patient) were a priori selected as important variables possibly influencing the survival function. After an elementary analysis of the 3 and 5 year survival fractions in section 2, a nonparametric estimation of the survival functions ignoring the effect of age is presented in section 3. In the last section COX'S (1972) proportional hazards model is used for a one dimensional regression on age which leads to the estimation of Si(tz), the survival function of patients with stage i and age z. This allows for a graphical comparison with the normal population. Finally some checks on the proportional hazard assumption are performed. The emphasis in this paper is on adequately applying and adapting (mostly existing) techniques, including the use of some generally available computer programs, to a practical case. Care has been given to model assumptions and theoretical foundations of the relevant methods.

Genugten, B.B. Van Der

doi: 10.1111/j.1467-9574.1983.tb00807.xpmid: N/A

Abstract In the linear regression model the generalized least squares (GLS) method is only applicable if the covariance matrix of the errors is known but for a scalar factor. Otherwise an estimator for this matrix has to be used. Then we speak of the estimated generalized least squares (EGLS) method. In this paper the asymptotic behaviour of both methods is compared. Results are applied to some standard models commonly used in econometrics

Smit, J.C.; Vervaat, W.

doi: 10.1111/j.1467-9574.1983.tb00808.xpmid: N/A

Abstract If X1, X2,… are exponentially distributed random variables thenσ∞k= 1 Xk=∞ with probability 1 iff σ∞k= 1 EXk=∞. This result, which is basic for a criterion in the theory of Markov jump processes for ruling out explosions (infinitely many transitions within a finite time) is usually proved under the assumption of independence (see FREEDMAN (1971), p. 153–154 or BREI‐MAN (1968), p. 337–338), but is shown in this note to hold without any assumption on the joint distribution. More generally, it is investigated when sums of nonnegative random variables with given marginal distributions converge or diverge whatever are their joint distributions.

doi: 10.1111/j.1467-9574.1983.tb00809.xpmid: N/A