On some dynamic generalized information measures for bivariate lifetimes

Several generalizations to the concept of Kullback-Leibler divergence measure and Kerridge inaccuracy measure are available in the literature. In a recent paper Kundu (Metrika, 78:415–435, 2015 Kundu, C. 2015. Generalized measures of information for truncated random variables. Metrika 78:415–35.[Crossref], [Web of Science ®] , [Google Scholar]) considered a generalized K-L divergence measure of order (α, β). Nath (Metrika, 13:123–135, 1968 Nath, P. 1968. Inaccuracy and coding theory. Metrika 13:123–35.[Crossref] , [Google Scholar]) has also proposed generalized inaccuracy measure of order α. Here we address the question of extending these measures to higher dimensions with reference to residual lifetimes. In the present work, the generalized divergence and inaccuracy measures are extended for conditional lifetimes of two components having possibly different ages. Several properties, including monotonicity, and bounds of these measures are obtained for conditional random variables. Moreover, we study the effect of (increasing) monotone transformation on these generalized measures.     

Product Life‐Cycle Management of Packaged Software

A software product becomes less valuable for its consumers over time due to technological and economic obsolescence. As a result, firms have an opportunity to introduce and sell upgrades that provide higher utility to consumers compared to an older and out‐of‐date software product. In a market that is growing and consists of homogeneous customers, we prove that the optimal upgrade intervals are monotonically increasing throughout the product's life cycle solely because of demand and cost considerations. This finding is in conformity with empirical evidence, thus validating our theoretical model. We then present comparative statics results to show that increase in the rate of obsolescence or network externalities may sometimes increase upgrade intervals for early upgrades and decrease these for later upgrades in the product's life cycle, but increase in market growth rate always decreases these intervals. Further, when successive software upgrades are forward compatible, upgrade intervals are longer than when they are not. Finally, we present three separate extensions of our model to showcase the robustness of our results. Since upgrade development costs depend on upgrade intervals, these insights help managers understand how costing for upgrades changes over the product's life cycle.     

Untransformed first observation problem in regression model with moving average process

This paper shows the impact of underestimation of variance of an estima-tor when first observation is left untransformed to simplify the computational procedure. In fact, the bias of the variance is not diminishing even for large sample size for the model considered. By partitioning the covariance matrix into two parts, this paper explains why least square estimator with untrans-formed first observation shows such a consequence. To demonstrate this, an exact GLS estimator is developed by modifying an approximate estimator. Nonetheless, the computational simplicity remains same.     

Determining Optimal Advertising Strategies: A Markov Decision Model Approach*

This study falls in the class of models in which advertising wearout and the differences between the learning and forgetting of advertisements are explicitly included. A discrete time Markov decision modeling approach is used to obtain optimal control limit policies, and an algorithm is provided to identify these policies. A control limit policy specifies whether or not to advertise in a specific time period on the basis of the level of awareness in that time period. Thus, the duration for which advertising is not done is determined endogenously, and the algorithm helps determine this duration for a given set of parameters. This is a particularly desirable feature, since advertising practitioners are interested in determining the optimal duration of advertising pulses. Computational experience suggests that the algorithm is very fast and easy to implement. Also, conditions on model parameters indicating the relative efficacy of pulsing versus uniform advertising are provided.