In this review, we will consider two closely related problems associated with the lognormal distribution: The approximation of the distribution of a lognormal sum (in the whole support) and the approximation of the Laplace transform of a lognormal distribution. The Laplace transform of the lognormal distribution can be employed to approximate the distribution of the lognormal sum via transform ...

In simulation, Median Polish Kriging is a technique used to predict unobserved data points in two-dimensional space. The linear behavior of the traditional Median Polish Kriging in the estimation of the mean function in a high grid makes the interpolation of O(1) which has a low order in the prediction and that leads to a high prediction error. Therefore, an improvement in the estimation of the...

Kriging interpolation is largely used in geostatistics to characterise the spatial structure of data and it is established in general based upon the stationary or intrinsic assumptions; however, the consequence of this second-order approximation is that the local singularities (or extremes) could be smoothed off. This drawback could be magnified as a finerscale phenomenon is being investigated,...

Kriging (Gaussian process, spatial correlation) metamodels approximate the Input/Output (I/O) functions implied by the underlying simulation models; such metamodels serve sensitivity analysis and optimization, especially for computationally expensive simulations. In practice, simulation analysts often know that the I/O function is monotonic. To obtain a Kriging metamodel that preserves this kno...

We have developed a domain agnostic ordinary kriging algorithm accessible via a standardsbased service-oriented architecture for sensor networks. We exploit the Open Geospatial Consortium (OGC) Sensor Web Enablement (SWE) standards. We need on-demand interpolation maps so runtime performance is a major priority. Our sensor data comes from wind in-situ observation stations in an area approximate...

For the six-wheel CRAB rover, this paper presents the torque control with Kriging estimation to improve the terrainability by minimizing wheel slip. In previous works, we presented a torque control approach, effectively improving terrainability by minimizing the variance of the required friction coefficient based on the static model. Using a Kalman filter to estimate the velocity information, a...

The research aim of this paper is to investigate the effectiveness of a new Kriging model which uses Taylor expansion to predict wireless network connectivity. Wireless network connectivity is measured by the strength of emitted signal power from the tower to the point in question. The prediction results are compared with those from the literature where an Ordinary Kriging model and a neural ne...

This paper focuses upon the efficient surrogate model algorithm for expensive simulation-based design optimization problems. Co-kriging method is used to develop a multi-fidelity surrogate model using two independent datasets. To achieve this objective, wing-body problem is taken as an example of application for highdimensional complex design problem. In addition, a simple sampling analysis is ...

In parametric modeling of loss distributions in actuarial science, a versatile choice with intermediate tail weight is the lognormal distribution. Surprisingly, however, the fitting of this model using estimators which are at once efficient and robust has not been seriously addressed in the extensive literature. Consequently, for example, typical estimators of the lognormal mean and variance fa...

The discovery of new exoplanets makes us wonder where each new exoplanet stands along its way to develop life as we know it on Earth. Our Evo-SETI Theory is a mathematical way to face this problem. We describe cladistics and evolution by virtue of a few statistical equations based on lognormal probability density functions (pdf) in the time. We call b-lognormal a lognormal pdf starting at insta...