The {2}-inverse with applications in statistics

On Burr III-Inverse Weibull Distribution with COVID-19 Applications

We introduce a flexible lifetime distribution called Burr III-Inverse Weibull (BIII-IW). The new proposed distribution has well-known sub-models. The BIII-IW density function includes exponential, left-skewed, right-skewed and symmetrical shapes. The BIII-IW model’s failure rate can be monotone and non-monotone depending on the parameter values. To show the importance of the BIII-IW distributio...

Inverse Problems in Statistics

Inverse Statistics in the Foreign Exchange Market

We investigate intra-day foreign exchange (FX) time series using the inverse statistic analysis developed in [1,2]. Specifically, we study the time-averaged distributions of waiting times needed to obtain a certain increase (decrease) ρ in the price of an investment. The analysis is performed for the Deutsch Mark (DM) against the $US for the full year of 1998, but similar results are obtained f...

Inverse Problems with Invariant Multiscale Statistics

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale scattering transform which discards the phase and thus exposes strong spectral correlations otherwise hidden beneath the phase fluctuations. As a result, bo...

Inverse Problems as Statistics

What mathematicians, scientists, engineers, and statisticians mean by \inverse problem" di ers. For a statistician, an inverse problem is an inference or estimation problem. The data are nite in number and contain errors, as they do in classical estimation or inference problems, and the unknown typically is in nite-dimensional, as it is in nonparametric regression. The additional complication i...