  Despite the availability of commercial QRNG devices, distinguishing between
PRNG and QRNG outputs computationally remains challenging. This paper presents
two significant contributions from the perspectives of QRNG manufacturers and
users. For manufacturers, the conventional method of assessing the quantumness
of single-photon-based QRNGs through mean and variance comparisons of photon
counts is statistically unreliable due to finite sample sizes. Given the
sub-Poissonian statistics of single photons, confirming the underlying
distribution is crucial for validating a QRNG's quantumness. We propose a more
efficient two-fold statistical approach to ensure the quantumness of optical
sources with the desired confidence level. Additionally, we demonstrate that
the output of QRNGs from exponential and uniform distributions exhibit
similarity under device noise, deriving corresponding photon statistics and
conditions for $\epsilon$-randomness.
  From the user's perspective, the fundamental parameters of a QRNG are
quantumness (security), efficiency (randomness and random number generation
rate), and cost. Our analysis reveals that these parameters depend on three
factors, expected photon count per unit time, external reference cycle
duration, and detection efficiency. A lower expected photon count enhances
security but increases cost and decreases the generation rate. A shorter
external reference cycle boosts security but must exceed a minimum threshold to
minimize timing errors, with minor impacts on cost and rate. Lower detection
efficiency enhances security and lowers cost but reduces the generation rate.
Finally, to validate our results, we perform statistical tests like NIST,
Dieharder, AIS-31, ENT etc. over the data simulated with different values of
the above parameters. Our findings can empower manufacturers to customize QRNGs
to meet user needs effectively.
