40 research outputs found
Testing Exponentiality Based on R\'enyi Entropy With Progressively Type-II Censored Data
We express the joint R\'enyi entropy of progressively censored order
statistics in terms of an incomplete integral of the hazard function, and
provide a simple estimate of the joint R\'enyi entropy of progressively Type-II
censored data. Then we establish a goodness of fit test statistic based on the
R\'enyi Kullback-Leibler information with the progressively Type-II censored
data, and compare its performance with the leading test statistic. A Monte
Carlo simulation study shows that the proposed test statistic shows better
powers than the leading test statistic against the alternatives with monotone
increasing, monotone decreasing and nonmonotone hazard functions.Comment: 16 page
Nonparametric inference about increasing odds rate distributions
To improve nonparametric estimates of lifetime distributions, we propose
using the increasing odds rate (IOR) model as an alternative to other popular,
but more restrictive, ``adverse ageing'' models, such as the increasing hazard
rate one. This extends the scope of applicability of some methods for
statistical inference under order restrictions, since the IOR model is
compatible with heavy-tailed and bathtub distributions. We study a strongly
uniformly consistent estimator of the cumulative distribution function of
interest under the IOR constraint. Numerical evidence shows that this estimator
often outperforms the classic empirical distribution function when the
underlying model does belong to the IOR family. We also study two different
tests, aimed at detecting deviations from the IOR property, and we establish
their consistency. The performance of these tests is also evaluated through
simulations
New Entropy Estimator with an Application to Test of Normality
In the present paper we propose a new estimator of entropy based on smooth
estimators of quantile density. The consistency and asymptotic distribution of
the proposed estimates are obtained. As a consequence, a new test of normality
is proposed. A small power comparison is provided. A simulation study for the
comparison, in terms of mean squared error, of all estimators under study is
performed
Statistical modeling of skewed data using newly formed parametric distributions
Several newly formed continuous parametric distributions are introduced to analyze skewed data. Firstly, a two-parameter smooth continuous lognormal-Pareto composite distribution is introduced for modeling highly positively skewed data. The new density is a lognormal density up to an unknown threshold value and a Pareto density for the remainder. The resulting density is similar in shape to the lognormal density, yet its upper tail is larger than the lognormal density and the tail behavior is quite similar to the Pareto density. Parameter estimation methods and the goodness-of-fit criterion for the new distribution are presented. A large actuarial data set is analyzed to illustrate the better fit and applicability of the new distribution over other leading distributions. Secondly, the Odd Weibull family is introduced for modeling data with a wide variety of hazard functions. This three-parameter family is derived by considering the distributions of the odds of the Weibull and inverse Weibull families. As a result, the Odd Weibull family is not only useful for testing goodness-of-fit of the Weibull and inverse Weibull as submodels, but it is also convenient for modeling and fitting different data sets, especially in the presence of censoring and truncation. This newly formed family not only possesses all five major hazard shapes: constant, increasing, decreasing, bathtub-shaped and unimodal failure rates, but also has wide variety of density shapes. The model parameters for exact, grouped, censored and truncated data are estimated in two different ways due to the fact that the inverse transformation of the Odd Weibull family does not change its density function. Examples are provided based on survival, reliability, and environmental sciences data to illustrate the variety of density and hazard shapes by analyzing complete and incomplete data. Thirdly, the two-parameter logistic-sinh distribution is introduced for modeling highly negatively skewed data with extreme observations. The resulting family provides not only negatively skewed densities with thick tails, but also variety of monotonic density shapes. The advantages of using the proposed family are demonstrated and compared by illustrating well-known examples. Finally, the folded parametric families are introduced to model the positively skewed data with zero data values
Modeling repairable system failure data using NHPP realiability growth mode.
Stochastic point processes have been widely used to describe the behaviour of repairable systems. The Crow nonhomogeneous Poisson process (NHPP) often known as the Power Law model is regarded as one of the best models for repairable systems. The goodness-of-fit test rejects the intensity function of the power law model, and so the log-linear model was fitted and tested for goodness-of-fit. The Weibull Time to Failure recurrent neural network (WTTE-RNN) framework, a probabilistic deep learning model for failure data, is also explored. However, we find that the WTTE-RNN framework is only appropriate failure data with independent and identically distributed interarrival times of successive failures, and so cannot be applied to nonhomogeneous Poisson process