The modeling of fertility patterns is an essential method researchers use to understand world-wide population patterns. Various types of fertility models have been reported in the literature to capture the patterns specific to developed countries. While much effort has been put into reducing...

Slowly varying regressors are asymptotically collinear in linear regression. Usual regression formulae for asymptotic standard errors remain valid but rates of convergence are affected and the limit distribution of the regression coefficients is shown to be one dimensional. Some asymptotic...

Consider independent and identically distributed random variables {X, Xn, n[set membership, variant]Zd+} with either EX=0 or E X=[infinity]. We establish strong laws so that [summation operator]n[less-than-or-equals, slant]N anXn/bN--1 almost surely. Our procedure selects the...

In this note, we give a closed-form expression in terms of the Lambert W function for the quantile function of the Gompertz–Makeham distribution. This probability distribution has frequently been used to describe human mortality and to establish actuarial tables. The analytical expression...

We provide procedures to generate random variables with Lindley distribution, and also with Poisson–Lindley or zero-truncated Poisson–Lindley distribution, as simple alternatives to the existing algorithms. Our procedures are based on the fact that the quantile functions of these probability...

According to integrated pest management for pests, we investigate the dynamic behavior of a class predator–prey system with state-dependent impulsive effects by releasing natural enemies and spraying pesticide at different thresholds. Using the Poincaré map and the properties of the Lambert W...

We illustrate the use of the Lambert W function by analysing two Economic Order Quantity (EOQ) scenarios: an EOQ model with perishable inventory; and a Net Present Value analysis of an EOQ problem with trim loss. Both scenarios are motivated by real-world situations. Via these two examples, we...

In this study, a novel exact technique is proposed for tracking the maximum power point (MPP) of photovoltaic (PV) modules connected in various configurations. The Lambert W function is used to perform the equations which express current–voltage (I–V), power–voltage (P–V) and...