Related papers: On an Inflated Unit-Lindley Distribution
We examine the calculation of density perturbation at large scales in the inflationary scenario. The formula for its magnitude is reviewed from first principles and applied to the original model of extended inflation. Our estimate is an…
We discuss the issue of setting appropriate initial conditions for inflation. Specifically, we consider natural inflation model and discuss the fine tuning required for setting almost homogeneous initial conditions over a region of order…
In this paper we propose a new lifetime model, called the odd generalized exponential linear failure rate distribution. Some statistical properties of the proposed distribution such as the moments, the quantiles, the median, and the mode…
In this article, I briefly review the status of infrared effects which occur when using inflationary models to calculate initial conditions for a subsequent hot, dense plasma phase. Three types of divergence have been identified in the…
For a given data set the problem of selecting either Lindley or xgamma distribution with unknown parameter is investigated in this article. Both these distributions can be used quite effectively for analyzing skewed non-negative data and in…
We consider models of inflection point inflation. The main drawback of such models is that they suffer from the overshoot problem. Namely the initial condition should be fine tuned to be near the inflection point for the universe to…
For an unknown continuous distribution on a real line, we consider the approximate estimation by the discretization. There are two methods for the discretization. First method is to divide the real line into several intervals before taking…
We review the connection between inflationary models and observations and concentrate to describe models based on softly broken supersymmetry, in particular running mass models, and their predictions. We then present a fit of the spectral…
Discrete ordinal responses such as Likert scales are regularly proposed in questionnaires and used as dependent variable in modeling. The response distribution for such scales is always discrete, with bounded support and often skewed. In…
We investigate multi-field inflationary scenarios with fields that drop out of the model in a staggered fashion. This feature is natural in certain multi-field inflationary setups within string theory; for instance, it can manifest itself…
A discrete version of the Gumbel (Type I) extreme value distribution has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It…
We consider small-field models which invoke the usual framework for the effective field theory, and large-field models which go beyond that. Present and future possibilities for discriminating between the models are assessed, on the…
It is already understood that the increasing observational evidence for an open Universe may be reconciled with inflation if our horizon is contained inside one single huge bubble nucleated during the inflationary phase transition. In the…
We explore the super-horizon evolution of the two-point and three-point correlation functions of the primordial density perturbation in randomly-generated multi-field potentials. We use the Transport method to evolve perturbations and give…
In this paper we introduce a new lifetime distribution by compounding exponential and Poisson-Lindley distributions, named exponential Poisson-Lindley distribution. Several properties are derived, such as density, failure rate, mean…
The family of primitive binary substitutions defined by $1 \mapsto 0 \mapsto 0 1^m$ with $m\in\mathbb{N}$ is investigated. The spectral type of the corresponding diffraction measure is analysed for its geometric realisation with prototiles…
In Brans-Dicke theory the Universe becomes divided after inflation into many exponentially large domains with different values of the effective gravitational constant. Such a process can be described by diffusion equations for the…
There exist several models of inflation that produce primordial bispectra that contain a large number of oscillations. In this paper we discuss these models, and aim at finding a method of detecting such bispectra in the data. We explain…
We derive limit theorems for the empirical distribution function of "devolatilized" increments of an It\^{o} semimartingale observed at high frequencies. These "devolatilized" increments are formed by suitably rescaling and truncating the…
Given a probability distribution $\mu$ a set $\Lambda (\mu)$ of positive real numbers is introduced, so that $\Lambda (\mu)$ measures the "divisibility" of $\mu$. The basic properties of $\Lambda (\mu)$ are described and examples of…