In this talk we review several applications of two Weibull extensions in statistical theory and applied research. The two extensions are the generalized Weibull and the exponentiated Weibull families, and the applications are in the areas of reliability and survival analysis, exteme value analysis, isotones and distributional approximations. 1 The Generalized Weibull Family The generalized Weib...

In this paper, we derive a simple and efficient matrix formulation using Laguerre polynomials to solve the singular integral equation with degenerate kernel. This method is based on replacement of unknown function by truncated series well known expansion functions. leads system algebraic equations coefficients. Thus, solving equation, coefficients are obtained. Some numerical examples included ...

In wood engineering, lower quantile estimation is vital to the safety of the construction with wood materials. In this thesis, we will first study the censored Weibull maximum likelihood estimate (MLE) of the lower quantile as in the current industrial standard D5457 (ASTM, 2004a) from a statistical point of view. According to our simulations, the lower quantile estimated by the censored Weibul...

The paper provides to reliability practitioners with a method (1) to estimate the robust Weibull family when the Taguchi method (TM) is applied, (2) to estimate the normal operational Weibull family in an accelerated life testing (ALT) analysis to give confidence to the extrapolation and (3) to perform the ANOVA analysis to both the robust and the normal operational Weibull family. On the other...

The instant system availability [Formula: see text] of a repairable system with the renewal equation was studied. The starting point monotonicity of [Formula: see text] was proved and the upper bound of [Formula: see text] is also derived. It was found that the interval of instant system availability monotonically decreases. In addition, we provide examples that validate the analytically derive...

Here, we look at the Sasa-Satsuma equation with M-truncated derivative (SSE-MTD). The analytical solutions in form of trigonometric, hyperbolic, elliptic, and rational functions are constructed using Jacobi elliptic function generalizing Riccati mapping methods. Because Sasa–Satsuma is applied to explain propagation femtosecond pulses optical fibers, acquired can be employed a wide range import...

The objective of this study was to evaluate the ability of three statistical distributions to characterize the vertical distribution of foliage mass in canopies of even-aged loblolly pine stands, based on airborne-scanning light detection and ranging (LiDAR) data. The functions were the Weibull and SB distributions and a mixture of the lognormal and Weibull distributions. Results indicated that...