In this paper, we develop some characterization results in terms of survival entropy of the first order statistic. In addition, we generalize the cumulative entropy recently proposed by Di Crescenzo and Logobardi (2009) to a new measure of information (called the failure entropy) and study some properties of it and its dynamic version. Furthermore, power distribution is characterized based on dynamic failure entropy.
Abstract. Background: Exposure to music during pregnancy enhances brain development and improves learning in neonatal rats. Methods: In these experiments, we examined the effects of exposure to silence, hard rock, classical, and rap music in utero plus 60 days postpartum on learning and memory in adult Wistar rats. Passive avoidance learning (PAL) was assessed at age 60 days, and a retention test was done 24 hours after training. Elevated plus maze (EPM) was also used as a standard behavioral task for assessing the effects of music therapy on anxiety. Furthermore, we measured serum corticosterone levels and adrenal weight at the end of experiments to show the possible effect of stress on the rats’ behavior. Results: Hard rock music impaired acquisition, increasing the number of trials to acquisition in PAL task. Hard rock music also impaired the retrieval process by decreasing step-through latency and increasing time spent in the dark compartment during the retention trial. Further, in the hard rock group, there were increases in serum corticosterone and adrenal weight of rats. Classical music, in turn, improved acquisition learning and retention memory and decreased serum corticosterone levels compared to the silence group. Rats’ exposure to rap music did not show any significant change in acquisition and retrieval processes compared to the silence group. In the EPM task, classical music exposure had anxiolytic-like effects revealed in an increase in the number of entries into open arms and time spent in the open arms. However, in this task, hard rock music induced an anxiogenic effect. Conclusions: Prenatal and postnatal exposure to music improves PAL and memory in adult rats. The effects of music therapy with classical music might be related to stress reduction by lowering corticosterone as a stress biomarker or anxiolytic effects; this deserves further examination.
Abstract. In this paper, we introduce new tests for exponentiality based on estimators of Renyi entropy of a continuous random variable. We first consider two transformations of the observations which turn the test of exponentiality into one of uniformity and use a corresponding test based on Renyi entropy. Critical values of the test statistics are computed by Monte Carlo simulations. Then, we compare powers of the tests for various alternatives and sample sizes with exponentiality tests based on Kullback-Leibler information proposed by Ebrahimi et al. (1992) and Choi et al. (2004). Our simulation results show that the proposed tests have higher powers than the competitor tests.
Abstract. Recently, a new distribution, named as extended generalized exponential distribution, has been introduced by Kundu and Gupta (2011). In this paper, we consider the extended generalized exponential distribution with known shape parameters α and β. At first, the exact expressions for marginal and product moments of order statistics are derived. Then, these values are used to obtain the necessary coefficients for the best linear unbiased estimators and L-moments estimators of the location and scale parameters. The mean squared errors of these estimators are also given and compared.
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