Random variable functions used in hydrology

In this work, expressions of the cumulative distribution function of Y X, Y/X and X/(X + Y ) for continuous dependent random variables with supported on a unbounded and bounded interval are derived. The dependence approach is based on copula functions. Additionally, the methodology is applied to real data on hydrology.En este trabajo, se derivan expresiones de la función de distribución acumulada de Y X, Y/X y X/(X + Y ) para variables aleatorias dependientes continuas con soporte en un intervalo ilimitado y limitado. El enfoque de dependencia se basa en funciones cópula. Además, la metodología se aplica a datos reales de hidrología

Bayesian analysis for the Lomax model using noninformative priors

The Lomax distribution is an important member in the distribution family. In this paper, we systematically develop an objective Bayesian analysis of data from a Lomax distribution. Noninformative priors, including probability matching priors, the maximal data information (MDI) prior, Jeffreys prior and reference priors, are derived. The propriety of the posterior under each prior is subsequently validated. It is revealed that the MDI prior and one of the reference priors yield improper posteriors, and the other reference prior is a second-order probability matching prior. A simulation study is conducted to assess the frequentist performance of the proposed Bayesian approach. Finally, this approach along with the bootstrap method is applied to a real data set

Testing For Aptitude-Treatment Interactions In Analysis Of Covariance And Randomized Block Designs Under Assumption Violations

This study compared the robustness of two analysis strategies designed to detect Aptitude-Treatment Interactions to two of their similarly-held assumptions, normality and residual variance homogeneity. The analysis strategies were the test of slope differences in analysis of covariance and the test of the Block-by- Treatment interaction in randomized block analysis of variance. With equal sample sizes in the treatment groups the results showed that residual variance heterogeneity has little effect on either strategy but nonnormality makes the test of slope differences liberal and the test of the Block-by-Treatment interaction conservative. With unequal sample sizes in the treatment groups the often-reported sample size-variance heterogeneity pairing is problematic for both strategies. The findings suggest that the randomized block strategy can be characterized as an overly-conservative alternative to the test of slope differences with respect to robustness

On the Distribution of the Product of Inverse Pareto and Exponential Random Variables

This article considers Inverse Pareto and Exponential distributions to create the distribution of the product. The researchers derived its properties, such as; survival functions and hazard functions, and used the model criterion such as Sum Square Error (SSE), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) in estimating the parameters for deriving the best joint distribution between monthly precipitation and temperature in the Philippines from 1974 to 2013. The results showed that considering the monthly precipitation and temperature data, the distribution of the product of Inverse Pareto and Exponential outperformed the other existing distribution of the product

THE IMPACT OF BONE MARROW TRANSPLANTION ON PATIENTS WITH PSYCHIATRIC DIAGNOSES: MEDICATION ADHERENCE ASSESSMENT

Objectives: We investigated whether there is a measurable difference in medication utilization for psychiatric conditions before and after bone marrow transplantation (BMT). Previous studies have identified a potential association between psychiatric conditions and immune function. We hypothesized that medication utilization for psychiatric diagnoses would be impacted by BMT. Methods: This study was a retrospective, quasi-experimental cohort design. De-identified data was compiled from the Truven database for patients ranging from January 2009 through December 2016. Two measurements of medication utilization, proportion of days covered (PDC) and medication possession ratio (MPR) were calculated for each included Medispan-defined class of medications before analyzing changes in PDC and MPR at the patient level. Results: Overall, 8,233 patients met the inclusion criteria. Across each measured medication class (anti-anxiety medications, anti-convulsants, antidepressant, hypnotic/sedatives, migraine medications and opioids) there was a statistically significant decrease in the number of raw prescriptions as well as in PDC value in the 2 years after BMT as compared to before the procedure. Conclusions: We found a decrease in medication utilization after BMT across the measured medication classes, indicating a potential resolution of psychiatric symptoms and a potential impact on the associated pathophysiology. These results provide support for the premise that genetic factors associated with immune function play a role in psychiatric illness

Mixed distributions with applications in finance and actuarial science

We study distributions connected with joint events (X, N), where X is the sum of N non-negative random variables {Xi}, which may be dependent or independent of N, and joint events (X, N, Y, M). In the latter, the X and Y are the sums of N and M non-negative random variables {Xi} and {Yi}, respectively. Models of this kind arise quite naturally in severalareas such as finance, actuarial science, hydro-climatic studies and others. In finance, the quantity N may represents a duration of growth in value of an investment, where a group of consecutive values of log-returns are of the same positive sign and X is its cumulative log-return. Inturn, the quantity M may represents a duration of decline in value of an investment, where a group of consecutive values of log-returns are of the same negative sign and Y is its cumulative log-return. In actuarial science, the N represents claim frequency and X represents the aggregate claim amount in a given time period. In clinical studies, N represents the number of hospital visits and X corresponds to the cumulative hospitalization cost. Our results include generalizations and formulation of bivariate and multivariate distributions that go beyond already existing models. In addition to theoretical results, we also consider the practical problem of parameter estimation using maximum likelihood, E-M algorithms, and simulation studies to validate our estimation strategies and application