1 Introduction and Overview Many problems in combinatorics, number theory, probability theory, reliability theory and statistics can be solved by applying a unifying method, which is known as the principle of inclusion-exclusion. The principle of inclusion-exclusion expresses the indicator function of a union of finitely many sets as an alternating sum of indicator functions of their intersecti...

OBJECTIVES Sinusoidal injury (SI) after oxaliplatin-based therapies for colorectal liver metastasis (CRLM) can increase postoperative morbidity. Preoperative methods to estimate SI are lacking. The aim of this study was to identify SI by evaluating portal vein haemodynamics. METHODS Magnetic resonance imaging flowmetry (MRIF) was used to estimate portal vein haemodynamics in 29 patients with ...

−∞ φ(t− ξ) · Φ(νt) dt, where φ and Φ are the pdf and cdf of N(0, 1), respectively. We derive two recurrence formulas for the effective computation of its values. We show that with an algorithm for this function, we can efficiently compute the second-order terms of Bonferroni-type inequalities yielding the upper and lower bounds for the distribution of a max-type binary segmentation statistic in...

MATERIAL & METHODS We have analyzed the loss of enamel and dentine after exposure to different non-alcoholic drinks with a simple new method using bovine teeth. 100 enamel and 100 dentine specimens from freshly extracted bovine incisors were randomly attributed to 10 groups (n=10 for enamel and dentine each). Prior to the start of the experiment all specimens were weighed using a precision bala...

1 θ + respectively. Shanker [3] has discussed its various mathematical and statistical properties including its shape, moment generating function, moments, skewness, kurtosis, hazard rate function, mean residual life function, stochastic orderings, mean deviations, distribution of order statistics, Bonferroni and Lorenz curves, Renyi entropy measure, stressstrength reliability , amongst others ...