scholarly journals Rational cubic Ball curves for monotone data

2016 ◽  
Author(s):  
Ayser Nasir Hassan Tahat ◽  
Abd Rahni Mt Piah ◽  
Zainor Ridzuan Yahya
Keyword(s):  
Monotone Data

scholarly journals GLOBAL CONTINUOUS SOLUTIONS FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LARGE AND MONOTONE DATA

2010 ◽  
Vol 07 (01) ◽  
pp. 139-164 ◽  
Author(s):  
AHMAD EL HAJJ ◽  
RÉGIS MONNEAU
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Hyperbolic System ◽  
Space Dimension ◽  
Continuous Solution ◽  
Hyperbolic Systems ◽  
Continuous Solutions ◽  
Dislocation Densities ◽  
Entropy Estimate ◽  
Monotone Data

In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and non-decreasing initial data. We remark that these results cover the case of systems which are hyperbolic but not strictly hyperbolic. Physically, this kind of diagonal hyperbolic system appears naturally in the modeling of the dynamics of dislocation densities.

scholarly journals Monotone data modeling using rational functions

2019 ◽  
Vol 27 (3) ◽  
pp. 2331-2343
Author(s):  
Zoha TARIQ ◽  
Farheen IBRAHEEM ◽  
Malik Zawwar HUSSAIN ◽  
Muhammad SARFRAZ
Keyword(s):  
Data Modeling ◽  
Rational Functions ◽  
Monotone Data

scholarly journals A monotone data augmentation algorithm for longitudinal data analysis via multivariate skew-t, skew-normal or t distributions

2019 ◽  
Vol 29 (6) ◽  
pp. 1542-1562 ◽  
Author(s):  
Yongqiang Tang
Keyword(s):  
Repeated Measures ◽  
Data Augmentation ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Monte Carlo Algorithm ◽  
Sensitivity Analyses ◽  
Special Cases ◽  
Monotone Data ◽  
T Distribution ◽  
Skew Normal

The mixed effects model for repeated measures has been widely used for the analysis of longitudinal clinical data collected at a number of fixed time points. We propose a robust extension of the mixed effects model for repeated measures for skewed and heavy-tailed data on basis of the multivariate skew-t distribution, and it includes the multivariate normal, t, and skew-normal distributions as special cases. An efficient Markov chain Monte Carlo algorithm is developed using the monotone data augmentation and parameter expansion techniques. We employ the algorithm to perform controlled pattern imputations for sensitivity analyses of longitudinal clinical trials with nonignorable dropouts. The proposed methods are illustrated by real data analyses. Sample SAS programs for the analyses are provided in the online supplementary material.

scholarly journals Monotone Data Visualization Using Rational Trigonometric Spline Interpolation

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Farheen Ibraheem ◽  
Maria Hussain ◽  
Malik Zawwar Hussain
Keyword(s):  
Data Visualization ◽  
Spline Interpolation ◽  
Trigonometric Functions ◽  
Rectangular Patch ◽  
Surface Data ◽  
Trigonometric Spline ◽  
Monotone Data ◽  
Cubic Function

Rational cubic and bicubic trigonometric schemes are developed to conserve monotonicity of curve and surface data, respectively. The rational cubic function has four parameters in each subinterval, while the rational bicubic partially blended function has eight parameters in each rectangular patch. The monotonicity of curve and surface data is retained by developing constraints on some of these parameters in description of rational cubic and bicubic trigonometric functions. The remaining parameters are kept free to modify the shape of curve and surface if required. The developed algorithm is verified mathematically and demonstrated graphically.

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