# FJRubio

## Recently Published

##### The Hyperbolic Secant Distribution
pdf, the cdf, the quantile function, random number generation, and moments associated to the Hyperbolic Secant distribution.
##### The family of two-piece distributions
This R markdown contains illustrative examples about the family of two-piece distributions and the "twopiece" R package.
##### The LogSumExp function
The LogSumExp function is the logarithm of the sum of the exponentials of n values. This R Markdown presents 5 methods to calculate the LogSumExp function.
##### The Power Generalised Weibull Distribution
The Power Generalised Weibull Distribution in R: a three-parameter distribution with positive support and flexible hazard function.
##### The Cox Proportional Hazards Model and the Partial Likelihood function
The Cox Proportional Hazards Model and the Partial Likelihood function
##### The Laplace Inverse Mills Ratio
R code and illustrations of the behaviour of the Laplace Inverse Mills Ratio (LIMR) and its first derivative.
##### Simulating survival times from a General Hazard structure with a flexible baseline hazard
This tutorial shows how to simulate from a General Hazard structure that includes time dependent effects as well as effects that only affect the hazard level.
##### Simulating from a Bivariate Gaussian Copula
R code to simulate from a bivariate distribution based on a Gaussian copula
##### The Kumaraswamy Distribution
pdf, the cdf, the quantile function, random number generation, and moments associated to the Kumaraswamy distribution.
##### Excess hazard models for insufficiently stratified life tables
A simulated data example
##### Likelihood Ratio Test: Skew Normal vs Normal
Description and implementation of the Likelihood Ratio Test for testing Normality vs skew-Normality. It also includes a simulation stud of the size and the power of the test when the sample size is 500. This simulation study shows that the LRT performs poorly (low power and wrong size) for this sample size, unless the null hypothesis is clearly false.
##### MLE Logistic Distribution
MLE for the location and scale parameters in the Logistic Distribution
##### t-intervals: unpaired observations
Life spans of wild type vs. transgenic mosquitoes
##### Paired differences: the Darwin data
t-intervals: paired observations
##### How many Monte Carlo simulations to get to an accurate estimate of a proportion?
Estimating a proportion $\theta$ and its relationship with the number of Monte Carlo simulations
##### Permutation test: examples
Some examples of permutation tests using the difference of means and the Kolmogorov-Smirnov test statistic
##### Robust Outlier Detection
Robust Outlier Detection vs. Non-Robust Outlier Detection
Mean vs. Median
##### Robust Estimation of Scale
Normalised Median Absolute Deviation vs. Standard Deviation
##### Binomial Trial: Bayesian Analysis
A Bayesian Analysis of a Binomial Trial.
##### Wald Confidence Interval for the Normal distribution
Second order approximation: Wald confidence intervals for the Normal distribution
##### A Brief analysis of the Challenger data
Analysis of the Challenger disaster data using logistic regression
##### Profile likelihood confidence intervals for the parameters of the normal distribution
Profile likelihood confidence intervals for the parameters of the normal distribution (mean and standard deviation)
##### Performance of normal Confidence Intervals for log-odds
A simulation study to check the performance of asymptotic normal CIs for the log-odds
##### Method of moments for the Kumaraswamy distribution
An example where the Method of Moments does not lead to a closed form solution and requires the use of numerical methods to obtain a solution to the corresponding estimating equations.
##### Logistic Regression: The Beetle data set
Maximum likelihood estimation in the logistic regression model
##### Numerical calculation of the Wasserstein-1 metric in 1-D: examples
Three examples of the numerical calculation of the Wasserstein-1 metric, including its use for comparing survival curves.
##### Parametric Excess Hazard Estimation: General Hazards
This R code illustrates the use of General Hazard structure models in a simulated data set. The data set was simulated using the General Hazards (GH) structure. The idea is to fit the parametric regression models with hazard structures PH, AH, AFT, and GH and select the one favoured by the Akaike Information Criterion (AIC).
##### Parametric Excess Hazard Estimation: Proportional Hazards
This R code illustrates the use of General Hazard structure models in a simulated data set. The data set was simulated using the Proportional Hazards (PH) structure. The idea is to fit the parametric regression models with hazard structures PH, AH, AFT, and GH and select the one favoured by the Akaike Information Criterion (AIC).
##### Frequentist vs Noninformative Bayesian inference in the Binomial model
Frequentist vs Noninformative Bayesian inference in the Binomial model using Uniform and Jeffreys priors.
##### Visual comparison of two populations
Some visual tools for comparing two univariate samples
##### Flexible linear mixed models: HIV-1 viral load after unstructured treatment interruption
A real data example of linear mixed models for censored responses with flexible random effects and flexible residual errors.
##### Flexible linear mixed models: Framingham study
A real data application of linear mixed models with flexible errors and flexible random effects.
##### How to create a random Secret Santa list in R
Two different methods to create a Secret Santa random list in R from a list of names.
##### An Introduction to MCMC
Illustration of some properties of MCMC samplers
##### Predictive Beta Binomial distribution
The predictive distribution for a Binomial sampling model with Beta prior.
##### The Normal-Normal Bayesian model (known variance)
The posterior distribution of the mean for a normal sampling model with known variance and normal prior distribution
##### The Beta-Binomial model
A short description of the Binomial distribution, the Beta distribution, and the Bayesian Beta-Binomial model.
##### The Inverse Mills Ratio
Some properties of the Inverse Mills Ratio
##### Kernel Density and Distribution Estimation for data with different supports
R codes to implement kernel density and distribution estimators for data with support on R, R_+, and (0,1) by using a transformation approach.
##### Bayesian Variable Selection: Analysis of DLD data
Tractable Bayesian Variable Selection: Beyond normality. Analysis of DLD data using two-piece residual errors and non-local priors.
##### The Generalised Weibull Distribution
Cumulative distribution function, quantile function, hazard function, and cumulative hazard function of the Generalised Weibull distribution.
##### The Exponentiated Weibull distribution
Probability density function, cumulative distribution function, quantile function, random number generation, hazard function, and cumulative hazard function of the Exponentiated Weibull distribution.
##### An objective prior for the number of degrees of freedom of a multivariate t distribution
An objective prior for the number of degrees of freedom of a multivariate t distribution
##### The Jeffreys prior for skew–symmetric models
The Jeffreys prior for the skewness parameter in skew–symmetric models
##### Kullback Leibler divergence between a multivariate t and a multivariate normal distributions
A tractable, scalable, expression for the Kullback Leibler divergence between a multivariate t and a multivariate normal distributions
##### Kullback Leibler divergence between two multivariate t distributions
A tractable, scalable, expression for the Kullback Leibler divergence between two multivariate t distributions
##### An application of an objective prior for the number of degrees of freedom of a multivariate t distribution
A financial application of an objective prior for the number of degrees of freedom of a multivariate t distribution
##### Nonparametric estimation of P(X<Y) for paired data
Several types of Nonparametric estimators of P(X<Y) for paired data
##### Galton’s Forecasting Competition
Galton’s Forecasting Competition data modelling using the DTP R package.
##### A weakly informative prior for the degrees of freedom of the t distribution
Implementation of a weakly informative prior for the degrees of freedom of the t distribution.
##### Mollified two-piece distributions
Mollification of two-piece distributions.
##### The Laplace and two-piece Laplace Distributions
Implementation of the Laplace and two piece Laplace distributions (using the R package twopiece).
##### Natural (non-) informative priors for the skew-normal distribution
Real data example to illustrate the use of Jeffreys and Total Variation priors for the shape parameter of the skew-normal distribution
##### t-copula with t and two piece t marginals
A real data example to illustrate how to fit a t-copula with t and two piece t marginals
##### TPSAS R Package
The TPSAS R package implements the univariate two-piece sinh–arcsinh distribution
##### Sinh-arcsinh distribution
Implementation of the probability density function, cumulative distribution function, quantile function, and random number generation of the SAS distribution.
##### Bayesian inference for the ratio of the means of two normals
Bayesian inference for the ratio of the means of two normal populations with unequal variances using reference priors.
##### Approximate Maximum Likelihood Estimation (AMLE)
A simple approach to maximum intractable likelihood estimation: AMLE. Two toy examples.
##### Ratio of two normals and a normal approximation
Implementaion of the distribution of the ratio of two independent normal distributions and a normal approximation.
##### Posterior QQ envelopes: normality test
Implementation of Posterior QQ envelopes for normality test.
##### Posterior QQ envelopes: Linear regression
Implementation of Posterior QQ envelopes and predictive QQ plots in the context of linear regression.
##### Flexible AFT Models III: Bayesian + two-piece
Bayesian AFT models with two-piece errors
##### Flexible AFT Models II: Bayesian + skew-symmetric
Bayesian Accelerated Failure Time models with skew-symmetric errors.
##### Flexible AFT Models I: MLE + two-piece
Accelerated failure time models with two-piece errors using maximum likelihood estimation.
##### twopiece R package with applications
The twopiece R package implements the family of Two-Piece distributions.
##### DTP R package
The DTP R package implements the family of Double Two-Piece distributions.
##### Two-piece Generalised Hyperbolic distribution
Description and implementation of the two-piece Generalised Hyperbolic distribution.
##### Two-piece Variance Gamma distribution
Implementation and description of the two-piece Variance Gamma distribution.
##### Two-piece Johnson-SU distribution
Implementation and description of the two-piece Johnson-SU distribution