10,242 research outputs found
The Generalized Weighted Lindley Distribution: Properties, Estimation and Applications
In this paper, we proposed a new lifetime distribution namely generalized
weighted Lindley (GLW) distribution. The GLW distribution is a useful
generalization of the weighted Lindley distribution, which accommodates
increasing, decreasing, decreasing-increasing-decreasing, bathtub, or unimodal
hazard functions, making the GWL distribution a flexible model for reliability
data. A significant account of mathematical properties of the new distribution
are presented. Different estimation procedures are also given such as, maximum
likelihood estimators, method of moments, ordinary and weighted least-squares,
percentile, maximum product of spacings and minimum distance estimators. The
different estimators are compared by an extensive numerical simulations.
Finally, we analyze two data sets for illustrative purposes, proving that the
GWL outperform several usual three parameters lifetime distributions
Exact solution to a Lindley-type equation on a bounded support
We derive the limiting waiting-time distribution of a model described
by the Lindley-type equation , where has a
polynomial distribution. This exact solution is applied to derive
approximations of when is generally distributed on a finite support.
We provide error bounds for these approximations.Comment: 9 pages, 2 figures, 1 table, 11 reference
A new two parameter lifetime distribution: model and properties
In this paper a new lifetime distribution which is obtained by compounding
Lindley and geometric distributions, named Lindley-geometric (LG) distribution,
is introduced. Several properties of the new distribution such as density,
failure rate, mean lifetime, moments, and order statistics are derived.
Furthermore, estimation by maximum likelihood and inference for large sample
are discussed. The paper is motivated by two applications to real data sets and
we hope that this model be able to attract wider applicability in survival and
reliability.Comment: arXiv admin note: text overlap with arXiv:1007.023
On queues with service and interarrival times depending on waiting times
We consider an extension of the standard G/G/1 queue, described by the
equation , where
and . For this model reduces to
the classical Lindley equation for the waiting time in the G/G/1 queue, whereas
for it describes the waiting time of the server in an alternating service
model. For all other values of this model describes a FCFS queue in which
the service times and interarrival times depend linearly and randomly on the
waiting times. We derive the distribution of when is generally
distributed and follows a phase-type distribution, and when is
exponentially distributed and deterministic.Comment: 19 pages, 1 figure, 24 reference
An alternating service problem
We consider a system consisting of a server alternating between two service
points. At both service points there is an infinite queue of customers that
have to undergo a preparation phase before being served. We are interested in
the waiting time of the server. The waiting time of the server satisfies an
equation very similar to Lindley's equation for the waiting time in the GI/G/1
queue. We will analyse this Lindley-type equation under the assumptions that
the preparation phase follows a phase-type distribution while the service times
have a general distribution. If we relax the condition that the server
alternates between the service points, then the model turns out to be the
machine repair problem. Although the latter is a well-known problem, the
distribution of the waiting time of the server has not been studied yet. We
shall derive this distribution under the same setting and we shall compare the
two models numerically. As expected, the waiting time of the server is on
average smaller in the machine repair problem than in the alternating service
system, but they are not stochastically ordered.Comment: 15 pages, 7 figures, 14 reference
On the one parameter unit-Lindley distribution and its associated regression model for proportion data
In this paper considering the transformation , where , we propose the unit-Lindley distribution and
investigate some of its mathematical properties. A important fact associated
with this new distribution is that is possible to obtain the analytical
expression for bias correction of the maximum likelihood estimator. Moreover,
it belongs to the exponential family. This distribution allows us to
incorporate covariates directly in the mean and consequently to quantify the
influence on the average of the response variable. Finally, a practical
application is present and it is shown that our model fits much better than the
Beta regression.Comment: 17 pages, 4 figure
The Utility of Reliability and Survival
Reliability (survival analysis, to biostatisticians) is a key ingredient for
mak- ing decisions that mitigate the risk of failure. The other key ingredient
is utility. A decision theoretic framework harnesses the two, but to invoke
this framework we must distinguish between chance and probability. We describe
a functional form for the utility of chance that incorporates all dispositions
to risk, and pro- pose a probability of choice model for eliciting this
utility. To implement the model a subject is asked to make a series of binary
choices between gambles and certainty. These choices endow a statistical
character to the problem of utility elicitation. The workings of our approach
are illustrated via a live example in- volving a military planner. The material
is general because it is germane to any situation involving the valuation of
chance
Some estimators of the PDF and CDF of the Lindley Distribution
This article addresses the different methods of estimation of the probability
density function (PDF) and the cumulative distribution function (CDF) for the
Lindley distribution. Following estimation methods are considered: uniformly
minimum variance unbiased estimator (UMVUE), maximum likelihood estimator
(MLE), percentile estimator (PCE), least square estimator (LSE), weighted least
square estimator (WLSE), Cram\'{e}r-von-Mises estimator (CVME),
Anderson-Darling estimator (ADE). Monte Carlo simulations are performed to
compare the performances of the proposed methods of estimation
Maximum Likelihood Estimation for the Weight Lindley Distribution Parameters under Different Types of Censoring
In this paper the maximum likelihood equations for the parameters of the
Weight Lindley distribution are studied considering different types of
censoring, such as, type I, type II and random censoring mechanism. A numerical
simulation study is perform to evaluate the maximum likelihood estimates. The
proposed methodology is illustrated in a real data set.Comment: 19 pg
A new probability model with support on unit interval: Structural properties, regression of bounded response and applications
A new distribution on (0, 1), generalized Log-Lindley distribution, is
proposed by extending the Log-Lindley distribution. This new distribution is
shown to be a weighted Log-Lindley distribution. Important probabilistic and
statistical properties have been derived. An interesting characterization of
the weighted distribution in terms of Kullback-Liebler distance and weighted
entropy has also been obtained. A useful result in insurance for the distorted
premium principal is presented and verified with numerical calculations. New
regression models for bounded responses based on this distribution and their
application is illustrated by considering modeling a real life data on risk
management and another data set on outpatient health expenditure in comparison
with beta regression and Log-Lindley regression models. Much better fits for
both data sets justify the relevance of the new distribution in statistical
modeling and analysis. Furthermore this generalization, apart from adding
flexibility for modelling, retains the compactness and tractability of
statistical quantities required for statistical analysis, which is a feature of
the Log-Lindley distribution. Thus, the generalized Log-Lindley distribution
should be a useful addition to statistical models for practitioners.Comment: 37 pages; 2 Figures, 3 Table, Pre-print Version-4.
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