Statistical sequential analysis for particle size distribution of magnetic nanoparticles

We present two statistical sequential analytical approaches to estimate particle size distribution of magnetic nanoparticles. They are termed sequential least square estimation and sequential linear minimum mean square error estimation, respectively. These approaches are implemented and quantified within the formalism of sequential estimation theory. The proposed methods are based on the data sampled sequentially in time and no matrix inversions are required in the implementation. To illustrate the efficiency of the proposed approaches, we give two examples of the particle size distributions in ferrofluid with normal sample and lognormal sample, respectively. In both cases we compare the reconstruction distributions using our methods with those calculated via the electron microscopy images of the ferrofluid particles.