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Hydraulic conductivity, a fundamental property in groundwater hydrology, plays a pivotal role in understanding subsurface flow dynamics and environmental assessments. Accurate estimation of hydraulic conductivity is essential for groundwater resource management, environmental impact assessments, and geotechnical engineering. This study delves into the assessment of different hydraulic conductivity estimation methods across diverse soil types and locations, with a specific emphasis on the influence of grain size. The research spans multiple study locations, each characterized by distinct soil types, ranging from coarse sands to fine gravels. Expected hydraulic conductivity ranges were established for each soil type, providing a critical benchmark for accuracy assessment. The study incorporates 16 widely used estimation methods, including Hazen, Hazen K (cm/s) = d10 (mm), Slichter, Terzaghi, Beyer, Sauerbrei, Kruger, Kozeny-Carmen, Zunker, Zamarin, USBR, Barr, and Alyamani and Sen, Chapuis, Krumbein and Monk, and Shepherd. These methods were selected based on their prevalence in groundwater modeling and geotechnical engineering. Findings from this research reveal significant variability in hydraulic conductivity estimations among the different methods. Notably, the Beyer, Zunker, and Shepherd methods consistently demonstrate superior accuracy across a range of soil types. Beyer's estimations align closely with the expected hydraulic conductivity ranges for various soil types, showcasing its applicability and reliability. Conversely, some methods, such as Zunker and Shepherd, yield estimations that deviate from expected ranges, particularly for fine gravel and coarse gravel. These discrepancies highlight the importance of method selection based on soil type and geological conditions. [ABSTRACT FROM AUTHOR]

This study aims to measure the dependence between individual lifetimes by applying multivariate Tweedie distribution to the lifetime data. Dependence between lifetimes incorporated in the mortality model is a new form of idea that gives significant impact on the risk of the annuity portfolio which is actually against the idea of standard actuarial methods that assumes independent between lifetimes. Hence, this paper applies Tweedie family distribution to the portfolio of lifetimes to induce the dependence between lives. Tweedie distribution is chosen since it contains symmetric and non-symmetric, as well as light-tailed and heavy-tailed distributions. Parameter estimation is modified in order to fit the Tweedie distribution to the data. This procedure is developed by using method of moments. In addition, the comparison stage is made to check for the adequacy between the observed mortality and expected mortality. Finally, the importance of including systematic mortality risk in the model is justified by the Pearson's chi-squared test. [ABSTRACT FROM AUTHOR]

Recently, crude oil price becomes volatile and have been the popular issue to be discussed in every country. Oil price fluctuations have major impact on the overall economy and finally will lead to increase in the inflation rate. It is important to describe these oil price fluctuations mathematically. This study aims to describe the above phenomena using geometric Brownian motion. Two crude oil prices, namely WTI and Brent have been analyzed based on daily oil price data from year 2000 until year 2015. Through the analysis using model assessment and model determination, crude oil price after year 2000 follows geometric Brownian motion process. We conclude that oil price fluctuations follow a geometric Brownian motion process without considering unexpected incidents. [ABSTRACT FROM AUTHOR]