Mahmood Ul Hassan. Foto: Statistiska institutionen

Mahmood Ul Hassan


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Works at Department of Statistics
Visiting address Universitetsvägen 10 B, plan 7
Room B 744
Postal address Statistiska institutionen 106 91 Stockholm

About me

Lecturer in Statistics.

Mottagningstid / Reception hours

Enligt överenskommelse / By appointment.


2019: PhD (Statistics)

Stockholm University, Stockholm, Sweden

Thesis Title: Achievement tests and optimal design for pretesting of questions.

2014: Master of Science in Statistics

Stockholm University, Stockholm, Sweden

Thesis Title: Fitting probability distributions to economic growth: a maximum likelihood approach.



A selection from Stockholm University publication database
  • 2016. Mahmood Ul Hassan, Pär Stockhammar. Journal of Applied Statistics 43 (9), 1583-1603

    The growth rate of the gross domestic product (GDP) usually carries heteroscedasticity, asymmetry and fat-tails. In this study three important and significantly heteroscedastic GDP series are examined. A Normal, normal-mixture, normal-asymmetric Laplace distribution and a Student's t-Asymmetric Laplace (TAL) distribution mixture are considered for distributional fit comparison of GDP growth series after removing heteroscedasticity. The parameters of the distributions have been estimated using maximum likelihood method. Based on the results of different accuracy measures, goodness-of-fit tests and plots, we find out that in the case of asymmetric, heteroscedastic and highly leptokurtic data the TAL-distribution fits better than the alternatives. In the case of asymmetric, heteroscedastic but less leptokurtic data the NM fit is superior. Furthermore, a simulation study has been carried out to obtain standard errors for the estimated parameters. The results of this study might be used in e.g. density forecasting of GDP growth series or to compare different economies.

  • 2019. Mahmood Ul Hassan, Frank Miller. Psychometrika 84 (4), 1101-1128

    Item calibration is a technique to estimate characteristics of questions (called items) for achievement tests. In computerized tests, item calibration is an important tool for maintaining, updating and developing new items for an item bank. To efficiently sample examinees with specific ability levels for this calibration, we use optimal design theory assuming that the probability to answer correctly follows an item response model. Locally optimal unrestricted designs have usually a few design points for ability. In practice, it is hard to sample examinees from a population with these specific ability levels due to unavailability or limited availability of examinees. To counter this problem, we use the concept of optimal restricted designs and show that this concept naturally fits to item calibration. We prove an equivalence theorem needed to verify optimality of a design. Locally optimal restricted designs provide intervals of ability levels for optimal calibration of an item. When assuming a two-parameter logistic model, several scenarios with D-optimal restricted designs are presented for calibration of a single item and simultaneous calibration of several items. These scenarios show that the naive way to sample examinees around unrestricted design points is not optimal.

  • 2019. Mahmood Ul Hassan, Frank Miller. Communications in statistics. Simulation and computation

    Achievement tests are used to characterize the proficiency of higher-education students. Item response theory (IRT) models are applied to these tests to estimate the ability of students (as latent variable in the model). In order for quality IRT parameters to be estimated, especially ability parameters, it is important that the appropriate number of dimensions is identified. Through a case study, based on a statistics exam for students in higher education, we show how dimensions and other model parameters can be chosen in a real situation. Our model choice is based both on empirical and on background knowledge of the test. We show that dimensionality influences the estimates of the item-parameters, especially the discrimination parameter which provides information about the quality of the item. We perform a simulation study to generalize our conclusions. Both the simulation study and the case study show that multidimensional models have the advantage to better discriminate between examinees. We conclude from the simulation study that it is safer to use a multidimensional model compared to a unidimensional if it is unknown which model is the correct one.

Show all publications by Mahmood Ul Hassan at Stockholm University

Last updated: February 27, 2020

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