In my coaching, I was told that the assumption of "uniform distribution of decrements" is no longer to be used. Instead of that, only the assumption "constant force of transition" is to be used. Using this assumption, the formula for converting independent rates to dependent rates was given as : (aq)x alpha = [ln(1- qx alpha)]*[1-((1-qx alpha)*(1-qx beta))] / [ln((1-qx alpha)*(1-qx beta))] Can someone kindly confirm, deny or edit this? Any help would be appreciated. Thankyou!
Hi, If we have two decrements alpha and beta with constant forces of transition A and B, the formula for leaving the population via decrement A over the year from age x to x+1 would be: A / B * (1 - (ap)x) as qx(alpha) = 1- exp(-A) -> A = -ln(1-qx(alpha)) different to your expression Similarly, B = -ln(1-qx(beta)) Hence A / B = -ln(1-qx(alpha)) / (-ln(1-qx(alpha)) - ln(1-qx(alpha))) different to your expression (ap)x = 1 - (aq)(A) - (aq)(B) = exp(-A - B) = 1-((1-qx(alpha))*(1-qx(beta))) same as your expression These formulae or variations of can be found on the summary page for the chapter on page 42. Joe
